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 re...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2017
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| Schriftenreihe: | Cambridge studies in advanced mathematics
163 |
| Links: | https://doi.org/10.1017/9781316675779 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (x, 200 Seiten) |
| ISBN: | 9781316675779 |
Internformat
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| spelling | Bovier, Anton 1957- Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany Cambridge Cambridge University Press 2017 1 Online-Ressource (x, 200 Seiten) txt c cr Cambridge studies in advanced mathematics 163 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. Erscheint auch als Druck-Ausgabe 9781107160491 |
| spellingShingle | Bovier, Anton 1957- Gaussian processes on trees from spin glasses to branching Brownian motion |
| title | Gaussian processes on trees from spin glasses to branching Brownian motion |
| title_auth | Gaussian processes on trees from spin glasses to branching Brownian motion |
| title_exact_search | Gaussian processes on trees from spin glasses to branching Brownian motion |
| title_full | Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany |
| title_fullStr | Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany |
| title_full_unstemmed | Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany |
| title_short | Gaussian processes on trees |
| title_sort | gaussian processes on trees from spin glasses to branching brownian motion |
| title_sub | from spin glasses to branching Brownian motion |
| work_keys_str_mv | AT bovieranton gaussianprocessesontreesfromspinglassestobranchingbrownianmotion |