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

Name: Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model
Brand: Springer Verlag, Singapore
SKU: 9789811002748
Price: 1374 CZK
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Autor: Makoto Katori

Jazyk:

Vazba: Brožovaná

Vydavatel: Springer Verlag, Singapore

Dostupnost: Skladem u dodavatele

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The purpose of this book is to introduce two recent topics in mathematical physics and probability t...

Informace o knize

Autor

Makoto Katori

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2015

Stránek

141

EAN

9789811002748

ISBN

9811002746

Enbook ID

02859360

Vydavatel

Springer Verlag, Singapore

Hmotnost

258

Rozměry

156 x 242 x 17

Kompletní popis

The purpose of this book is to introduce two recent topics in mathematical physics and probability theory: the Schramm-Loewner evolution (SLE) and interacting particle systems related to random matrix theory. A typical example of the latter systems is Dyson's Brownian motion (BM) model. The SLE and Dyson's BM model may be considered as "children" of the Bessel process with parameter D , BES( D ), and the SLE and Dyson's BM model as "grandchildren" of BM. In Chap. 1 the parenthood of BM in diffusion processes is clarified and BES( D ) is defined for any D _ 1. Dependence of the BES( D ) path on its initial value is represented by the Bessel flow. In Chap. 2 SLE is introduced as a complexification of BES( D ). Rich mathematics and physics involved in SLE are due to the nontrivial dependence of the Bessel flow on D . From a result for the Bessel flow, Cardy's formula in Carleson's form is derived for SLE. In Chap. 3 Dyson's BM model with parameter _ is introduced as a multivariate extension of BES( D ) with the relation D = _ + 1. The book concentrates on the case where _ = 2 and calls this case simply the Dyson model. 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.

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

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