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Gaussian Processes on Trees
Anton Bovier
其他書名
From Spin Glasses to Branching Brownian Motion
出版Cambridge University Press, 2017
主題Mathematics / Probability & Statistics / GeneralMathematics / Probability & Statistics / Stochastic ProcessesScience / Physics / Mathematical & Computational
ISBN11071604999781107160491
URLhttp://books.google.com.hk/books?id=2qoODQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.