Random Graph Dynamics

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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.

Random Graph Dynamics

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 9780521866569
Total Pages : 222 pages
Book Rating : 4.8/5 (665 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 2006-10-23 with total page 222 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 about the same 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. While this literature is extensive, many of the papers are based on simulations and nonrigorous arguments. 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 of this book is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Random Graphs and Complex Networks

Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 110717287X
Total Pages : 341 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Random Graphs and Complex Networks by : Remco van der Hofstad

Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2016-12-22 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Dynamics on Graphs

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 9781009521451
Total Pages : 0 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Dynamics on Graphs by : Rick Durrett

Download or read book Dynamics on Graphs written by Rick Durrett and published by Cambridge University Press. This book was released on 2024-10-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extensive revision of the 2007 book 'Random Graph Dynamics,' covering the current state of mathematical research in the field, is ideal for researchers and graduate students. It considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs. However, it investigates a wide variety of dynamics. The author describes results for the convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Chapter 8 discusses a new challenging and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.

Random Graphs

Author : Béla Bollobás
Publisher : Cambridge University Press
ISBN 13 : 9780521797221
Total Pages : 520 pages
Book Rating : 4.7/5 (972 download)

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Book Synopsis Random Graphs by : Béla Bollobás

Download or read book Random Graphs written by Béla Bollobás and published by Cambridge University Press. This book was released on 2001-08-30 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised and updated version of the classic first edition.

Small Worlds

Author : Duncan J. Watts
Publisher : Princeton University Press
ISBN 13 : 0691188335
Total Pages : 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 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Generating Random Networks and Graphs

Author : Anthony C. C. Coolen
Publisher : Oxford University Press
ISBN 13 : 0198709897
Total Pages : 325 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Generating Random Networks and Graphs by : Anthony C. C. Coolen

Download or read book Generating Random Networks and Graphs written by Anthony C. C. Coolen and published by Oxford University Press. This book was released on 2017 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes how to correctly and efficiently generate random networks based on certain constraints. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'.

Probability on Graphs

Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Probability on Graphs by : Geoffrey Grimmett

Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

Random Operators

Author : Michael Aizenman
Publisher : American Mathematical Soc.
ISBN 13 : 1470419130
Total Pages : 326 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 326 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.

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

Author : Maria Eulália Vares
Publisher : Springer Nature
ISBN 13 : 3030607542
Total Pages : 819 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius by : Maria Eulália Vares

Download or read book In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius written by Maria Eulália Vares and published by Springer Nature. This book was released on 2021-03-25 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

Complex Graphs and Networks

Author : Fan Chung
Publisher : American Mathematical Soc.
ISBN 13 : 0821836579
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complex Graphs and Networks by : Fan Chung

Download or read book Complex Graphs and Networks written by Fan Chung and published by American Mathematical Soc.. This book was released on 2006 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.

Exponential Random Graph Models for Social Networks

Author : Dean Lusher
Publisher : Cambridge University Press
ISBN 13 : 0521193567
Total Pages : 361 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Exponential Random Graph Models for Social Networks by : Dean Lusher

Download or read book Exponential Random Graph Models for Social Networks written by Dean Lusher and published by Cambridge University Press. This book was released on 2013 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account of the theoretical and methodological underpinnings of exponential random graph models (ERGMs).

A Dynamical Approach to Random Matrix Theory

Author : László Erdős
Publisher : American Mathematical Soc.
ISBN 13 : 1470436485
Total Pages : 226 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 226 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.

Graph Theoretic Methods in Multiagent Networks

Author : Mehran Mesbahi
Publisher : Princeton University Press
ISBN 13 : 1400835356
Total Pages : 424 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Graph Theoretic Methods in Multiagent Networks by : Mehran Mesbahi

Download or read book Graph Theoretic Methods in Multiagent Networks written by Mehran Mesbahi and published by Princeton University Press. This book was released on 2010-07-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA

The Structure and Dynamics of Networks

Author : Mark Newman
Publisher : Princeton University Press
ISBN 13 : 1400841356
Total Pages : 593 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Structure and Dynamics of Networks by : Mark Newman

Download or read book The Structure and Dynamics of Networks written by Mark Newman and published by Princeton University Press. This book was released on 2011-10-23 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society. But what exactly is a network? What different types of networks are there? Why are they interesting, and what can they tell us? In recent years, scientists from a range of fields--including mathematics, physics, computer science, sociology, and biology--have been pursuing these questions and building a new "science of networks." This book brings together for the first time a set of seminal articles representing research from across these disciplines. It is an ideal sourcebook for the key research in this fast-growing field. The book is organized into four sections, each preceded by an editors' introduction summarizing its contents and general theme. The first section sets the stage by discussing some of the historical antecedents of contemporary research in the area. From there the book moves to the empirical side of the science of networks before turning to the foundational modeling ideas that have been the focus of much subsequent activity. The book closes by taking the reader to the cutting edge of network science--the relationship between network structure and system dynamics. From network robustness to the spread of disease, this section offers a potpourri of topics on this rapidly expanding frontier of the new science.

Graph Directed Markov Systems

Author : R. Daniel Mauldin
Publisher : Cambridge University Press
ISBN 13 : 9780521825382
Total Pages : 302 pages
Book Rating : 4.8/5 (253 download)

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Book Synopsis Graph Directed Markov Systems by : R. Daniel Mauldin

Download or read book Graph Directed Markov Systems written by R. Daniel Mauldin and published by Cambridge University Press. This book was released on 2003-08-07 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.

The Random-Cluster Model

Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 3540328912
Total Pages : 392 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Random-Cluster Model by : Geoffrey R. Grimmett

Download or read book The Random-Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.