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Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 11)

DOI: 10.1007/978-981-10-0275-5

ISBN: 978-981-10-0274-8

Publisher: Springer Singapore - Springer Journals

Feb 9, 2016

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Chapter 1Bessel Processes

Katori, Makoto

Pages: 1 –39

[Basic notions of probability theory and stochastic analysis are explained using the Brownian motion and its functionals. The concepts of probability space and filtration are introduced, and the strong Markov property and the martingale property of Brownian motion are explained. A diffusion...
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Chapter 2Schramm–Loewner Evolution (SLE)

Katori, Makoto

Pages: 41 –56

[We consider the Loewner chain, which is a time evolution of a conformal transformation defined on the upper-half complex plane. The chain is driven by a given continuous real function of time t and it determines a path γ\documentclass[12pt]{minimal} \usepackage{amsmath}...
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Chapter 3Dyson Model

Katori, Makoto

Pages: 57 –137

[Dyson’s Brownian motion model is a one-parameter (β>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...

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