Overview
- Discusses the new trend in which complex analysis is applied, in contrast to original probability theory and statistical mechanics
- Includes new topics such as the Schramm–Loewner evolution and the random matrix theory
- Relates topics not only to probability theory and statistical mechanics but also to quantum integrable systems, representation theory, enumerative combinatorics, conformal field theory, and functional analysis
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 11)
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Table of contents (3 chapters)
Keywords
About this book
The Dyson model inherits the two aspects of BES(3); hence it has very strong solvability. That is, the process is proved to be determinantal in the sense that all spatio-temporal correlation functions are given by determinants, and all of them are controlled by a single function called the correlation kernel. From the determinantal structure of the Dyson model, the Tracy–Widom distribution is derived.
Authors and Affiliations
Bibliographic Information
Book Title: Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model
Authors: Makoto Katori
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-981-10-0275-5
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2016
Softcover ISBN: 978-981-10-0274-8Published: 16 February 2016
eBook ISBN: 978-981-10-0275-5Published: 08 February 2016
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: X, 141
Number of Illustrations: 16 illustrations in colour
Topics: Mathematical Physics, Probability Theory and Stochastic Processes, Complex Systems, Statistical Physics and Dynamical Systems