[PDF] Large Deviations For Random Graphs eBook

Author : Sourav Chatterjee
Publisher : Springer
Page : 175 pages
File Size : 38,51 MB
Release : 2017-08-31
Category : Mathematics
ISBN : 3319658166

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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.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 341 pages
File Size : 47,61 MB
Release : 2017
Category : Computers
ISBN : 110717287X

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

Author : Alan Frieze
Publisher : Cambridge University Press
Page : 483 pages
File Size : 12,86 MB
Release : 2016
Category : Mathematics
ISBN : 1107118506

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

Author : Béla Bollobás
Publisher : Cambridge University Press
Page : 520 pages
File Size : 47,93 MB
Release : 2001-08-30
Category : Mathematics
ISBN : 9780521797221

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This is a revised and updated version of the classic first edition.

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 203 pages
File Size : 37,89 MB
Release : 2010-05-31
Category : Mathematics
ISBN : 1139460889

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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.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 507 pages
File Size : 17,90 MB
Release : 2024-02-08
Category : Mathematics
ISBN : 1107174007

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The definitive introduction to the local and global structure of random graph models for complex networks.

Author : Neil O'Connell
Publisher :
Page : 15 pages
File Size : 21,16 MB
Release : 1996
Category : Graph theory
ISBN :

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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.)."

Author : Alice Guionnet
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 42,94 MB
Release : 2009-03-25
Category : Mathematics
ISBN : 3540698965

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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.