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Large Deviations for Random Graphs

École d'Été de Probabilités de Saint-Flour XLV - 2015

  • Book
  • © 2017

Overview

Authors:
  1. Sourav Chatterjee

    1. Department of Statistics, Stanford University, Stanford, USA

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  • 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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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Sourav Chatterjee
    Pages 1-6

  3. Preparation

    • Sourav Chatterjee
    Pages 7-25

  4. Basics of Graph Limit Theory

    • Sourav Chatterjee
    Pages 27-41

  5. Large Deviation Preliminaries

    • Sourav Chatterjee
    Pages 43-51

  6. Large Deviations for Dense Random Graphs

    • Sourav Chatterjee
    Pages 53-70

  7. Applications of Dense Graph Large Deviations

    • Sourav Chatterjee
    Pages 71-97

  8. Exponential Random Graph Models

    • Sourav Chatterjee
    Pages 99-117

  9. Large Deviations for Sparse Graphs

    • Sourav Chatterjee
    Pages 119-164

  10. Back Matter

    Pages 165-170
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Keywords

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.







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

  • Department of Statistics, Stanford University, Stanford, USA

    Sourav Chatterjee

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