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Gaussian Processes on Trees

Gaussian Processes on Trees
From Spin Glasses to Branching Brownian Motion


Part of Cambridge Studies in Advanced Mathematics

  • Author: Anton Bovier, Rheinische Friedrich-Wilhelms-Universität Bonn
  • Date Published: November 2016
  • availability: In stock
  • format: Hardback
  • isbn: 9781107160491

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About the Authors
  • 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.

    • A comprehensive presentation that will help graduates to enter this active area of research
    • Elucidates connections between extreme value theory, statistical mechanics of spin glasses, and branching Brownian motion (BBM)
    • Summarises a large body of work on BBM
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    Reviews & endorsements

    '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, 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, Zentralblatt MATH

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    Product details

    • Date Published: November 2016
    • format: Hardback
    • isbn: 9781107160491
    • length: 210 pages
    • dimensions: 235 x 157 x 16 mm
    • weight: 0.44kg
    • contains: 4 b/w illus.
    • availability: In stock
  • Table of Contents

    1. Extreme value theory for iid sequences
    2. Extremal processes
    3. Normal sequences
    4. Spin glasses
    5. Branching Brownian motion
    6. Bramson's analysis of the F-KPP equation
    7. The extremal process of BBM
    8. Full extremal process
    9. Variable speed BBM

  • Author

    Anton Bovier, Rheinische Friedrich-Wilhelms-Universität Bonn
    Anton Bovier is Professor of Mathematics at the University of Bonn. He is the author of more than 130 scientific papers and two monographs, Statistical Mechanics of Disordered Systems: A Mathematical Perspective (Cambridge, 2006) and Metastability: A Potential-Theoretic Approach (with Frank den Hollander, 2016). Bovier is a Fellow of the Institute of Mathematical Statistics and a member of the Clusters of Excellence, The Hausdorff Center for Mathematics and ImmunoSensation, both at the University of Bonn.

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