Large Deviations For Random Graphs

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Large Deviations for Random Graphs

Author : Sourav Chatterjee
Publisher : Springer
ISBN 13 : 3319658166
Total Pages : 175 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Large Deviations for Random Graphs by : Sourav Chatterjee

Download or read book Large Deviations for Random Graphs written by Sourav Chatterjee and published by Springer. This book was released on 2017-08-31 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Large Deviations in Randomly Coloured Random Graphs

Author : J. D. Biggins
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (538 download)

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Book Synopsis Large Deviations in Randomly Coloured Random Graphs by : J. D. Biggins

Download or read book Large Deviations in Randomly Coloured Random Graphs written by J. D. Biggins and published by . This book was released on 2003 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Some Large Deviation Results for Sparse Random Graphs

Author : Neil O'Connell
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (458 download)

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Book Synopsis Some Large Deviation Results for Sparse Random Graphs by : Neil O'Connell

Download or read book Some Large Deviation Results for Sparse Random Graphs written by Neil O'Connell and published by . This book was released on 1996 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We obtain a large deviation principle (LDP) for the relative size of the largest connected component in a random graph with small edge probability. The rate function, which is not convex in general, is determined explicitly using a new technique. As a corollary we present an asymptotic formula for the probability that the random graph is connected. We also present an LDP and related result for the number of isolated vertices. Here we make use of a simple but apparently unknown characterisation, wheich is obtained by embedding the random graph in a random directed graph. The results demonstrate that, at this scaling, the properties 'connected' and 'contains no isolated vertices' are not asymptotically equivalent. (At the threshold probability they are asymptotically equivalent.)."

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 2017 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.

Large Deviations Principle on the Mixing Times of Exponential Random Graph Models

Author : Peter F. Shu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)

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Book Synopsis Large Deviations Principle on the Mixing Times of Exponential Random Graph Models by : Peter F. Shu

Download or read book Large Deviations Principle on the Mixing Times of Exponential Random Graph Models written by Peter F. Shu and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Random Graphs

Author : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1107118506
Total Pages : 483 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Random Graphs by : Alan Frieze

Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Random Graphs

Author : Svante Janson
Publisher : John Wiley & Sons
ISBN 13 : 1118030966
Total Pages : 350 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Random Graphs by : Svante Janson

Download or read book Random Graphs written by Svante Janson and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references

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 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.

Random Graphs and Complex Networks

Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 1107174007
Total Pages : 507 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 2024-02-08 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive introduction to the local and global structure of random graph models for complex networks.

Particle Systems, Random Media and Large Deviations

Author : Richard Durrett
Publisher : American Mathematical Soc.
ISBN 13 : 0821850423
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Particle Systems, Random Media and Large Deviations by : Richard Durrett

Download or read book Particle Systems, Random Media and Large Deviations written by Richard Durrett and published by American Mathematical Soc.. This book was released on 1985 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Strange Logic of Random Graphs

Author : Joel Spencer
Publisher : Springer Science & Business Media
ISBN 13 : 3662045389
Total Pages : 167 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis The Strange Logic of Random Graphs by : Joel Spencer

Download or read book The Strange Logic of Random Graphs written by Joel Spencer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

A Large-deviations Principle for All the Components in a Sparse Inhomogeneous Random Graph

Author : Luisa Andreis
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis A Large-deviations Principle for All the Components in a Sparse Inhomogeneous Random Graph by : Luisa Andreis

Download or read book A Large-deviations Principle for All the Components in a Sparse Inhomogeneous Random Graph written by Luisa Andreis and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Probability of Large Deviations of Random Variables

Author : I. N. Sanov
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis On the Probability of Large Deviations of Random Variables by : I. N. Sanov

Download or read book On the Probability of Large Deviations of Random Variables written by I. N. Sanov and published by . This book was released on 1958 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Large random matrices

Author : Alice Guionnet
Publisher : Springer Science & Business Media
ISBN 13 : 3540698965
Total Pages : 296 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Large random matrices by : Alice Guionnet

Download or read book Large random matrices written by Alice Guionnet and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graph Theory and Additive Combinatorics

Author : Yufei Zhao
Publisher : Cambridge University Press
ISBN 13 : 1009310933
Total Pages : 336 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Graph Theory and Additive Combinatorics by : Yufei Zhao

Download or read book Graph Theory and Additive Combinatorics written by Yufei Zhao and published by Cambridge University Press. This book was released on 2023-07-31 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

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.