Gaussian Processes on Trees

From Spin Glasses to Branching Brownian Motion

AvAnton Bovier

Inbunden, Engelska, 2016

Del 163 i serien Cambridge Studies in Advanced Mathematics

847 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-11-07
Mått:157 x 235 x 16 mm
Vikt:440 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:210
Förlag:Cambridge University Press
ISBN:9781107160491

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.