Gaussian Processes on Trees
From Spin Glasses to Branching Brownian Motion

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 & 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

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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