Large deviations for random graphs
Author(s)
Bibliographic Information
Large deviations for random graphs
(Lecture notes in mathematics, 2197 . École d'été de probabilités de Saint-Flour ; 45-2015)
Springer, c2017
Available at / 40 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2197200037158900
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
1. Introduction.- 2. Preparation.- 3. Basics of graph limit theory.- 4. Large deviation preliminaries.- 5. Large deviations for dense random graphs.- 6. Applications of dense graph large deviations.- 7. Exponential random graph models.- 8. Large deviations for sparse graphs.- Index.
by "Nielsen BookData"