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Gaussian Processes on Trees

Gaussian Processes on Trees
From Spin Glasses to Branching Brownian Motion

$69.99 (P)

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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    Product details

    • Date Published: November 2016
    • format: Hardback
    • isbn: 9781107160491
    • length: 210 pages
    • dimensions: 235 x 157 x 16 mm
    • weight: 0.42kg
    • 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
    References
    Index.

  • 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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