Dynamics And Randomness

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Random Graph Dynamics

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Random Graph Dynamics by : Rick Durrett

Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

P-adic Deterministic and Random Dynamics

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
ISBN 13 : 1402026609
Total Pages : 279 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis P-adic Deterministic and Random Dynamics by : Andrei Y. Khrennikov

Download or read book P-adic Deterministic and Random Dynamics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

Dynamics and Randomness

Author : Alejandro Maass
Publisher : Springer Science & Business Media
ISBN 13 : 9401003459
Total Pages : 279 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Dynamics and Randomness by : Alejandro Maass

Download or read book Dynamics and Randomness written by Alejandro Maass and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each chapter for their well prepared manuscripts and the stimulating conferences they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book.

Random Dynamical Systems

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 3662128780
Total Pages : 590 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Random Dynamical Systems by : Ludwig Arnold

Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Topological Dynamics of Random Dynamical Systems

Author : Nguyen Dinh Cong
Publisher : Oxford University Press
ISBN 13 : 9780198501572
Total Pages : 216 pages
Book Rating : 4.5/5 (15 download)

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Book Synopsis Topological Dynamics of Random Dynamical Systems by : Nguyen Dinh Cong

Download or read book Topological Dynamics of Random Dynamical Systems written by Nguyen Dinh Cong and published by Oxford University Press. This book was released on 1997 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic treatment of the theory of topological dynamics of random dynamical systems. A relatively new field, the theory of random dynamical systems unites and develops the classical deterministic theory of dynamical systems and probability theory, finding numerous applications in disciplines ranging from physics and biology to engineering, finance and economics. This book presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.

Dynamics of Gambling: Origins of Randomness in Mechanical Systems

Author : Jaroslaw Strzalko
Publisher : Springer
ISBN 13 : 364203960X
Total Pages : 160 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Dynamics of Gambling: Origins of Randomness in Mechanical Systems by : Jaroslaw Strzalko

Download or read book Dynamics of Gambling: Origins of Randomness in Mechanical Systems written by Jaroslaw Strzalko and published by Springer. This book was released on 2010-01-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our everyday life is in?uenced by many unexpected (dif?cult to predict) events usually referred as a chance. Probably, we all are as we are due to the accumulation point of a multitude of chance events. Gambling games that have been known to human beings nearly from the beginning of our civilization are based on chance events. These chance events have created the dream that everybody can easily become rich. This pursuit made gambling so popular. This book is devoted to the dynamics of the mechanical randomizers and we try to solve the problem why mechanical device (roulette) or a rigid body (a coin or a die) operating in the way described by the laws of classical mechanics can behave in such a way and produce a pseudorandom outcome. During mathematical lessons in primary school we are taught that the outcome of the coin tossing experiment is random and that the probability that the tossed coin lands heads (tails) up is equal to 1/2. Approximately, at the same time during physics lessons we are told that the motion of the rigid body (coin is an example of suchabody)isfullydeterministic. Typically,studentsarenotgiventheanswertothe question Why this duality in the interpretation of the simple mechanical experiment is possible? Trying to answer this question we describe the dynamics of the gambling games based on the coin toss, the throw of the die, and the roulette run.

Random Operators

Author : Michael Aizenman
Publisher : American Mathematical Soc.
ISBN 13 : 1470419130
Total Pages : 343 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Random Operators by : Michael Aizenman

Download or read book Random Operators written by Michael Aizenman and published by American Mathematical Soc.. This book was released on 2015-12-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Random Perturbations of Dynamical Systems

Author : M. I. Freidlin
Publisher : Springer Science & Business Media
ISBN 13 : 1468401769
Total Pages : 334 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Random Perturbations of Dynamical Systems by : M. I. Freidlin

Download or read book Random Perturbations of Dynamical Systems written by M. I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

Small Worlds

Author : Duncan J. Watts
Publisher : Princeton University Press
ISBN 13 : 0691188335
Total Pages : 279 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Small Worlds by : Duncan J. Watts

Download or read book Small Worlds written by Duncan J. Watts and published by Princeton University Press. This book was released on 2018-06-05 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone knows the small-world phenomenon: soon after meeting a stranger, we are surprised to discover that we have a mutual friend, or we are connected through a short chain of acquaintances. In his book, Duncan Watts uses this intriguing phenomenon--colloquially called "six degrees of separation"--as a prelude to a more general exploration: under what conditions can a small world arise in any kind of network? The networks of this story are everywhere: the brain is a network of neurons; organisations are people networks; the global economy is a network of national economies, which are networks of markets, which are in turn networks of interacting producers and consumers. Food webs, ecosystems, and the Internet can all be represented as networks, as can strategies for solving a problem, topics in a conversation, and even words in a language. Many of these networks, the author claims, will turn out to be small worlds. How do such networks matter? Simply put, local actions can have global consequences, and the relationship between local and global dynamics depends critically on the network's structure. Watts illustrates the subtleties of this relationship using a variety of simple models---the spread of infectious disease through a structured population; the evolution of cooperation in game theory; the computational capacity of cellular automata; and the sychronisation of coupled phase-oscillators. Watts's novel approach is relevant to many problems that deal with network connectivity and complex systems' behaviour in general: How do diseases (or rumours) spread through social networks? How does cooperation evolve in large groups? How do cascading failures propagate through large power grids, or financial systems? What is the most efficient architecture for an organisation, or for a communications network? This fascinating exploration will be fruitful in a remarkable variety of fields, including physics and mathematics, as well as sociology, economics, and biology.

A Dynamical Approach to Random Matrix Theory

Author : László Erdős
Publisher : American Mathematical Soc.
ISBN 13 : 1470436485
Total Pages : 239 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Dynamical Approach to Random Matrix Theory by : László Erdős

Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Dynamics and Randomness II

Author : Alejandro Maass
Publisher : Springer Science & Business Media
ISBN 13 : 9781402019906
Total Pages : 244 pages
Book Rating : 4.0/5 (199 download)

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Book Synopsis Dynamics and Randomness II by : Alejandro Maass

Download or read book Dynamics and Randomness II written by Alejandro Maass and published by Springer Science & Business Media. This book was released on 2004-05-31 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the lectures given at the Second Conference on Dynamics and Randomness held at the Centro de Modelamiento Matemático of the Universidad de Chile, from December 9-13, 2003. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. The courses were on: -Some Aspects of Random Fragmentations in Continuous Times; -Metastability of Ageing in Stochastic Dynamics; -Algebraic Systems of Generating Functions and Return Probabilities for Random Walks; -Recurrent Measures and Measure Rigidity; -Stochastic Particle Approximations for Two-Dimensional Navier Stokes Equations; and -Random and Universal Metric Spaces. The intended audience for this book is Ph.D. students on Probability and Ergodic Theory as well as researchers in these areas. The particular interest of this book is the broad areas of problems that it covers. We have chosen six main topics and asked six experts to give an introductory course on the subject touching the latest advances on each problem.

Stable and Random Motions in Dynamical Systems

Author : Jurgen Moser
Publisher : Princeton University Press
ISBN 13 : 1400882699
Total Pages : 216 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Stable and Random Motions in Dynamical Systems by : Jurgen Moser

Download or read book Stable and Random Motions in Dynamical Systems written by Jurgen Moser and published by Princeton University Press. This book was released on 2016-03-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Stochastic Dynamics

Author : Hans Crauel
Publisher : Springer Science & Business Media
ISBN 13 : 0387226559
Total Pages : 457 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Stochastic Dynamics by : Hans Crauel

Download or read book Stochastic Dynamics written by Hans Crauel and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.

Handbook of Dynamics and Probability

Author : Peter Müller
Publisher : Springer Nature
ISBN 13 : 3030884864
Total Pages : 544 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Handbook of Dynamics and Probability by : Peter Müller

Download or read book Handbook of Dynamics and Probability written by Peter Müller and published by Springer Nature. This book was released on 2021-11-20 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our time is characterized by an explosive growth in the use of ever more complicated and sophisticated (computer) models. These models rely on dynamical systems theory for the interpretation of their results and on probability theory for the quantification of their uncertainties. A conscientious and intelligent use of these models requires that both these theories are properly understood. This book is to provide such understanding. It gives a unifying treatment of dynamical systems theory and probability theory. It covers the basic concepts and statements of these theories, their interrelations, and their applications to scientific reasoning and physics. The book stresses the underlying concepts and mathematical structures but is written in a simple and illuminating manner without sacrificing too much mathematical rigor. The book is aimed at students, post-docs, and researchers in the applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many technical aspects covered in appendices, but does require some basic knowledge in analysis, linear algebra, and physics. Peter Müller, now a professor emeritus at the University of Hawaii, has worked extensively on ocean and climate models and the foundations of complex system theories.

Domain Structured Chaos and Applications

Author : Marat Akhmet
Publisher : IOP Publishing Limited
ISBN 13 : 9780750335058
Total Pages : 150 pages
Book Rating : 4.3/5 (35 download)

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Book Synopsis Domain Structured Chaos and Applications by : Marat Akhmet

Download or read book Domain Structured Chaos and Applications written by Marat Akhmet and published by IOP Publishing Limited. This book was released on 2021-08-04 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain structured dynamics introduces a way for analysis of chaos in fractals, neural networks and random processes. It starts with newly invented abstract similarity sets and maps, which are in the basis of the abstract similarity dynamics. Then a labeling procedure is designed to determine the domain structured dynamics. The results follow the Pythagorean doctrine, considering finite number of indices for the labeling, with potential to become universal in future. The immediate power of the approach for fractals as domains of chaos, revisited famous deterministic and stochastic models, new types of differential equations and neural networks is seen in the book. This is not considered through widening areas, where the notions can be seen and recognized, but by deepening abstraction. Key Features Provides the abstract similarity map, which generalizes the Bernoulli shift for abstract self-similar sets. Discusses dynamically generated self-similar sets as a method of chaos generation. Introduces abstract fractals as sets of metric spaces on the basis of abstract similar sets. Presents fractals concepts discussed through the newly introduced notions.

Determinism and Randomness in Quantum Dynamics

Author : Göran Lindblad
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (186 download)

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Book Synopsis Determinism and Randomness in Quantum Dynamics by : Göran Lindblad

Download or read book Determinism and Randomness in Quantum Dynamics written by Göran Lindblad and published by . This book was released on 1992 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Dynamics of Structures

Author : Jie Li
Publisher : John Wiley & Sons
ISBN 13 : 0470824255
Total Pages : 426 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Stochastic Dynamics of Structures by : Jie Li

Download or read book Stochastic Dynamics of Structures written by Jie Li and published by John Wiley & Sons. This book was released on 2009-07-23 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures. Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters. "The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution." —A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA "The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field." —Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA