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.Additional ISBNs1107160499, 1316871258, 9781107160491, 9781316871256Gaussian Processes on Trees: From Spin Glasses to Branching Brownian Motion is written by Anton Bovier and published by Cambridge University Press. ISBNs for Gaussian Processes on Trees are 9781316871256, 1316871258 and the print ISBNs are 9781107160491, 1107160499. Additional ISBNs include 1107160499, 1316871258, 9781107160491, 9781316871256.