Large Deviations For Random Graphs

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Large Deviations For Random Graphs

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Author : Sourav Chatterjee
language : en
Publisher: Springer
Release Date : 2017-08-31

Large Deviations For Random Graphs written by Sourav Chatterjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Mathematics categories.

This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.

Random Graphs And Complex Networks

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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2017

Random Graphs And Complex Networks written by Remco van der Hofstad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Computers categories.

This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Introduction To Random Graphs

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Author : Alan Frieze
language : en
Publisher: Cambridge University Press
Release Date : 2016

Introduction To Random Graphs written by Alan Frieze and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Particle Systems Random Media And Large Deviations

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Author : Richard Durrett
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Particle Systems Random Media And Large Deviations written by Richard Durrett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.

Random Graphs And Complex Networks Volume 2

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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-08

Random Graphs And Complex Networks Volume 2 written by Remco van der Hofstad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-08 with Mathematics categories.

Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

Random Graphs

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Author : Alan Frieze
language : en
Publisher:
Release Date : 1992

Random Graphs written by Alan Frieze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Random graphs categories.

Entropy Large Deviations And Statistical Mechanics

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Author : Richard.S. Ellis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Entropy Large Deviations And Statistical Mechanics written by Richard.S. Ellis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of indepen dent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure conver gence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly.

Large Deviations In Randomly Coloured Random Graphs

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Author : J. D. Biggins
language : en
Publisher:
Release Date : 2003

Large Deviations In Randomly Coloured Random Graphs written by J. D. Biggins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Random graphs categories.

Large Random Matrices

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Author : Alice Guionnet
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-25

Large Random Matrices written by Alice Guionnet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-25 with Mathematics categories.

These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

Random Graphs

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Author : V. F. Kolchin
language : en
Publisher: Cambridge University Press
Release Date : 1999

Random Graphs written by V. F. Kolchin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Results of research on classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields.