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  1. Home
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  3. Gaussian Processes on Trees
  • Cited by 29
  • Anton Bovier, Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher:
Cambridge University Press
Online publication date:
November 2016
Print publication year:
2016
Online ISBN:
9781316675779
DOI:
https://doi.org/10.1017/9781316675779
Subjects:
Mathematics (general), Mathematics, Mathematical Physics, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Studies in Advanced Mathematics (163)
Information

Book description

Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.

Reviews

'The text is a very well-written presentation of the motivations and recent developments in the study of the extreme process of the BBM. This provides a perfect guide for any researcher interested in this field, especially those who are looking for a relatively quick introduction.'

Bastien Mallein Source: Mathematical Reviews

'When discussing most of the questions, the author pays good attention to both ideas and techniques. He presents a large number of results, many of them are non-trivial limit theorems. Some results are classical in the field, others are quite new, published very recently. While some of the results belong to the author, credit is given to several other contributors in the area. Besides the many results given with their proofs, the author includes useful bibliographical notes in the end of each chapter. The book ends with a comprehensive list of 117 references and Index. This is a well-written book on hot topics from modern stochastics and its applications. The book can be recommended to researchers and university graduate students.'

Jordan M. Stoyanov Source: Zentralblatt MATH

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Contents

Contents
References
References
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