Large Deviations for Random Graphs

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

  • Sourav Chatterjee

Part of the Lecture Notes in Mathematics book series (LNM, volume 2197)

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2197)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Sourav Chatterjee
    Pages 1-6
  3. Sourav Chatterjee
    Pages 7-25
  4. Sourav Chatterjee
    Pages 27-41
  5. Sourav Chatterjee
    Pages 43-51
  6. Sourav Chatterjee
    Pages 53-70
  7. Sourav Chatterjee
    Pages 71-97
  8. Sourav Chatterjee
    Pages 99-117
  9. Sourav Chatterjee
    Pages 119-164
  10. Back Matter
    Pages 165-170

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Sourav Chatterjee
    • 1
  1. 1.Department of StatisticsStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65816-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-65815-5
  • Online ISBN 978-3-319-65816-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book