000 01982aam a2200205 4500
008 170511b2017 xxu||||| |||| 00| 0 eng d
020 _a9781107160491
082 _a519.23
100 _aBovier, Anton
245 _aGaussian processes on trees: from spin glasses to branching Brownian motion
_cBovier, Anton
260 _bCambridge university press
300 _ax, 200 p.
440 _aCambridge studies in advanced mathematics
504 _aTable 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.
520 _aBranching 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. https://www.goodreads.com/book/show/32971791-gaussian-processes-on-trees
650 _aRandom variables
650 _aGaussian processes
650 _aBranching Brownian motion
942 _2ddc
999 _c206344