Large Deviations for Random Graphs

Beschreibung

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.

First book-length treatment of large deviations for random graphs, plus a chapter on exponential random graphs

Contains a summary of important results from graph limit theory with complete proofs

Written in a style for beginning graduate students, self-contained with essentially no need for background knowledge other than some amount of graduate probability and analysis

Autor*in

Sourav Chatterjee

Themen in »Large Deviations for Random Graphs«

Random graph Large deviations Erdos-Renyi graph Exponential random graph Graph limit theory Graphon combinatorics

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“This nice book is recommended to all probabilists who wish to study the beautiful theory of large deviations for random graphs.” (Zakhar Kabluchko, Mathematical Reviews, April, 2018)
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