Overview
- 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
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2197)
Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)
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About this book
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.
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Keywords
Table of contents (8 chapters)
Reviews
“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)
Authors and Affiliations
Bibliographic Information
Book Title: Large Deviations for Random Graphs
Book Subtitle: École d'Été de Probabilités de Saint-Flour XLV - 2015
Authors: Sourav Chatterjee
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-65816-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-65815-5Published: 02 September 2017
eBook ISBN: 978-3-319-65816-2Published: 31 August 2017
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XI, 170
Topics: Probability Theory and Stochastic Processes, Combinatorics