Random Matrices And Iterated Random Functions

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Random Matrices and Iterated Random Functions

Author : Gerold Alsmeyer
Publisher : Springer Science & Business Media
ISBN 13 : 364238806X
Total Pages : 265 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Random Matrices and Iterated Random Functions by : Gerold Alsmeyer

Download or read book Random Matrices and Iterated Random Functions written by Gerold Alsmeyer and published by Springer Science & Business Media. This book was released on 2013-08-28 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry, and dynamical systems. A great deal of recent work has focused on the study of spectra of large random matrices on the one hand and on iterated random functions, especially random difference equations, on the other. However, the methods applied in these two research areas are fairly dissimilar. Motivated by the idea that tools from one area could potentially also be helpful in the other, the volume editors have selected contributions that present results and methods from random matrix theory as well as from the theory of iterated random functions. This work resulted from a workshop that was held in Münster, Germany in 2011. The aim of the workshop was to bring together researchers from two fields of probability theory: random matrix theory and the theory of iterated random functions. Random matrices play fundamental, yet very different roles in the two fields. Accordingly, leading figures and young researchers gave talks on their field of interest that were also accessible to a broad audience.

Branching Random Walks

Author : Zhan Shi
Publisher : Springer
ISBN 13 : 3319253727
Total Pages : 143 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Branching Random Walks by : Zhan Shi

Download or read book Branching Random Walks written by Zhan Shi and published by Springer. This book was released on 2016-02-04 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.

Random Matrices and Iterated Random Functions

Author : Gerold Alsmeyer
Publisher :
ISBN 13 : 9783642388071
Total Pages : 276 pages
Book Rating : 4.3/5 (88 download)

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Book Synopsis Random Matrices and Iterated Random Functions by : Gerold Alsmeyer

Download or read book Random Matrices and Iterated Random Functions written by Gerold Alsmeyer and published by . This book was released on 2013-09-30 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Iterated Random Functions

Author : Persi Diaconis
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (785 download)

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Book Synopsis Iterated Random Functions by : Persi Diaconis

Download or read book Iterated Random Functions written by Persi Diaconis and published by . This book was released on 1998 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Models with Power-Law Tails

Author : Dariusz Buraczewski
Publisher : Springer
ISBN 13 : 3319296795
Total Pages : 325 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Stochastic Models with Power-Law Tails by : Dariusz Buraczewski

Download or read book Stochastic Models with Power-Law Tails written by Dariusz Buraczewski and published by Springer. This book was released on 2016-07-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.

Recent Trends in Ergodic Theory and Dynamical Systems

Author : Siddhartha Bhattacharya
Publisher : American Mathematical Soc.
ISBN 13 : 1470409313
Total Pages : 272 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Trends in Ergodic Theory and Dynamical Systems by : Siddhartha Bhattacharya

Download or read book Recent Trends in Ergodic Theory and Dynamical Systems written by Siddhartha Bhattacharya and published by American Mathematical Soc.. This book was released on 2015-01-26 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Recent Trends in Ergodic Theory and Dynamical Systems, in honor of S. G. Dani's 65th Birthday, held December 26-29, 2012, in Vadodara, India. This volume covers many topics of ergodic theory, dynamical systems, number theory and probability measures on groups. Included are papers on Teichmüller dynamics, Diophantine approximation, iterated function systems, random walks and algebraic dynamical systems, as well as two surveys on the work of S. G. Dani.

A Lifetime of Excursions Through Random Walks and Lévy Processes

Author : Loïc Chaumont
Publisher : Springer Nature
ISBN 13 : 3030833097
Total Pages : 354 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis A Lifetime of Excursions Through Random Walks and Lévy Processes by : Loïc Chaumont

Download or read book A Lifetime of Excursions Through Random Walks and Lévy Processes written by Loïc Chaumont and published by Springer Nature. This book was released on 2022-01-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.

Free Probability and Random Matrices

Author : James A. Mingo
Publisher : Springer
ISBN 13 : 1493969420
Total Pages : 343 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Free Probability and Random Matrices by : James A. Mingo

Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.

Hyperbolic Dynamics, Fluctuations and Large Deviations

Author : D. Dolgopyat
Publisher : American Mathematical Soc.
ISBN 13 : 1470411121
Total Pages : 354 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hyperbolic Dynamics, Fluctuations and Large Deviations by : D. Dolgopyat

Download or read book Hyperbolic Dynamics, Fluctuations and Large Deviations written by D. Dolgopyat and published by American Mathematical Soc.. This book was released on 2015-04-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the semester-long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland. The broad theme of the program was the long-term behavior of dynamical systems and their statistical behavior. During the last 50 years, the statistical properties of dynamical systems of many different types have been the subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on many different areas in mathematics, physics, engineering and biology. The papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas such as statistical physics, spectral theory and some aspects of number theory and geometry.

The Mathematics of Shuffling Cards

Author : Persi Diaconis
Publisher : American Mathematical Society
ISBN 13 : 1470463032
Total Pages : 360 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Mathematics of Shuffling Cards by : Persi Diaconis

Download or read book The Mathematics of Shuffling Cards written by Persi Diaconis and published by American Mathematical Society. This book was released on 2023-03-20 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a lively development of the mathematics needed to answer the question, “How many times should a deck of cards be shuffled to mix it up?” The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table. The mathematics ranges from probability (Markov chains) to combinatorics (symmetric function theory) to algebra (Hopf algebras). There are applications to magic tricks and gambling along with a careful comparison of the mathematics to the results of real people shuffling real cards. The book explores links between shuffling and higher mathematics—Lie theory, algebraic topology, the geometry of hyperplane arrangements, stochastic calculus, number theory, and more. It offers a useful springboard for seeing how probability theory is applied and leads to many corners of advanced mathematics. The book can serve as a text for an upper division course in mathematics, statistics, or computer science departments and will be appreciated by graduate students and researchers in mathematics, statistics, and computer science, as well as magicians and people with a strong background in mathematics who are interested in games that use playing cards.

Algorithms and Models for the Web Graph

Author : Anthony Bonato
Publisher : Springer
ISBN 13 : 3319131230
Total Pages : 170 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Algorithms and Models for the Web Graph by : Anthony Bonato

Download or read book Algorithms and Models for the Web Graph written by Anthony Bonato and published by Springer. This book was released on 2014-11-12 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Workshop on Algorithms and Models for the Web Graph, WAW 2014, held in Beijing, China, in December 2014. The 12 papers presented were carefully reviewed and selected for inclusion in this volume. The aim of the workshop was to further the understanding of graphs that arise from the Web and various user activities on the Web, and stimulate the development of high-performance algorithms and applications that exploit these graphs. The workshop gathered the researchers who are working on graph-theoretic and algorithmic aspects of related complex networks, including social networks, citation networks, biological networks, molecular networks, and other networks arising from the Internet.

Handbook of Elasticity Solutions

Author : Mark L. Kachanov
Publisher : Springer Science & Business Media
ISBN 13 : 9781402014727
Total Pages : 760 pages
Book Rating : 4.0/5 (147 download)

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Book Synopsis Handbook of Elasticity Solutions by : Mark L. Kachanov

Download or read book Handbook of Elasticity Solutions written by Mark L. Kachanov and published by Springer Science & Business Media. This book was released on 2003-11-30 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook is intended as a desk reference for researchers, students and engineers working in various areas of solid mechanics and quantitative materials science. It contains a broad range of elasticity solutions. In particular, it covers the following topics: -Basic equations in various coordinate systems, -Green's functions for isotropic and anisotropic solids, -Cracks in two- and three-dimensional solids, -Eshelby's problems and related results, -Stress concentrations at inhomogeneities, -Contact problems, -Thermoelasticity. The solutions have been collected from a large number of monographs and research articles. Some of the presented results were obtained only recently and are not easily available. All solutions have been thoroughly checked and transformed to a userfriendly form.

Diffusion Processes and Related Problems in Analysis, Volume II

Author : V. Wihstutz
Publisher : Springer Science & Business Media
ISBN 13 : 1461203899
Total Pages : 344 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Diffusion Processes and Related Problems in Analysis, Volume II by : V. Wihstutz

Download or read book Diffusion Processes and Related Problems in Analysis, Volume II written by V. Wihstutz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.

Modeling Multi-Level Systems

Author : Octavian Iordache
Publisher : Springer
ISBN 13 : 3642179460
Total Pages : 244 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Modeling Multi-Level Systems by : Octavian Iordache

Download or read book Modeling Multi-Level Systems written by Octavian Iordache and published by Springer. This book was released on 2011-02-05 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to modeling of multi-level complex systems, a challenging domain for engineers, researchers and entrepreneurs, confronted with the transition from learning and adaptability to evolvability and autonomy for technologies, devices and problem solving methods. Chapter 1 introduces the multi-scale and multi-level systems and highlights their presence in different domains of science and technology. Methodologies as, random systems, non-Archimedean analysis, category theory and specific techniques as model categorification and integrative closure, are presented in chapter 2. Chapters 3 and 4 describe polystochastic models, PSM, and their developments. Categorical formulation of integrative closure offers the general PSM framework which serves as a flexible guideline for a large variety of multi-level modeling problems. Focusing on chemical engineering, pharmaceutical and environmental case studies, the chapters 5 to 8 analyze mixing, turbulent dispersion and entropy production for multi-scale systems. Taking inspiration from systems sciences, chapters 9 to 11 highlight multi-level modeling potentialities in formal concept analysis, existential graphs and evolvable designs of experiments. Case studies refer to separation flow-sheets, pharmaceutical pipeline, drug design and development, reliability management systems, security and failure analysis. Perspectives and integrative points of view are discussed in chapter 12. Autonomous and viable systems, multi-agents, organic and autonomic computing, multi-level informational systems, are revealed as promising domains for future applications. Written for: engineers, researchers, entrepreneurs and students in chemical, pharmaceutical, environmental and systems sciences engineering, and for applied mathematicians.

Self-similar and Self-affine Sets and Measures

Author : Balázs Bárány
Publisher : American Mathematical Society
ISBN 13 : 1470470462
Total Pages : 466 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Self-similar and Self-affine Sets and Measures by : Balázs Bárány

Download or read book Self-similar and Self-affine Sets and Measures written by Balázs Bárány and published by American Mathematical Society. This book was released on 2023-11-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.

Products of Random Matrices

Author : Andrea Crisanti
Publisher : Springer Science & Business Media
ISBN 13 : 3642849423
Total Pages : 172 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Products of Random Matrices by : Andrea Crisanti

Download or read book Products of Random Matrices written by Andrea Crisanti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the present moment, after the success of the renormalization group in providing a conceptual framework for studying second-order phase tran sitions, we have a nearly satisfactory understanding of the statistical me chanics of classical systems with a non-random Hamiltonian. The situation is completely different if we consider the theory of systems with a random Hamiltonian or of chaotic dynamical systems. The two fields are connected; in fact, in the latter the effects of deterministic chaos can be modelled by an appropriate stochastic process. Although many interesting results have been obtained in recent years and much progress has been made, we still lack a satisfactory understanding of the extremely wide variety of phenomena which are present in these fields. The study of disordered or chaotic systems is the new frontier where new ideas and techniques are being developed. More interesting and deep results are expected to come in future years. The properties of random matrices and their products form a basic tool, whose importance cannot be underestimated. They playa role as important as Fourier transforms for differential equations. This book is extremely interesting as far as it presents a unified approach for the main results which have been obtained in the study of random ma trices. It will become a reference book for people working in the subject. The book is written by physicists, uses the language of physics and I am sure that many physicists will read it with great pleasure.

Advances in Cryptology - ASIACRYPT 2000

Author : Tatsuaki Okamoto
Publisher : Springer
ISBN 13 : 3540444483
Total Pages : 641 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Advances in Cryptology - ASIACRYPT 2000 by : Tatsuaki Okamoto

Download or read book Advances in Cryptology - ASIACRYPT 2000 written by Tatsuaki Okamoto and published by Springer. This book was released on 2003-06-26 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: ASIACRYPT 2000 was the sixth annual ASIACRYPT conference. It was sp- sored by the International Association for Cryptologic Research (IACR) in - operation with the Institute of Electronics, Information, and Communication Engineers (IEICE). The ?rst conference with the name ASIACRYPT took place in 1991, and the series of ASIACRYPT conferences were held in 1994, 1996, 1998, and 1999, in cooperation with IACR. ASIACRYPT 2000 was the ?rst conference in the series to be sponsored by IACR. The conference received 140 submissions (1 submission was withdrawn by the authors later), and the program committee selected 45 of these for presen- tion. Extended abstracts of the revised versions of these papers are included in these proceedings. The program also included two invited lectures by Thomas Berson (Cryptography Everywhere: IACR Distinguished Lecture) and Hideki Imai (CRYPTREC Project – Cryptographic Evaluation Project for the Japanese Electronic Government). Abstracts of these talks are included in these proce- ings. The conference program also included its traditional “rump session” of short, informal or impromptu presentations, kindly chaired by Moti Yung. Those p- sentations are not re?ected in these proceedings. The selection of the program was a challenging task as many high quality submissions were received. The program committee worked very hard to evaluate the papers with respect to quality, originality, and relevance to cryptography. I am extremely grateful to the program committee members for their en- mous investment of time and e?ort in the di?cult and delicate process of review and selection.