Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model. 1st ed. 2016

種類:

電子ブック

責任表示:

by Makoto Katori

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2016

著者名:

• Katori, Makoto.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematical Physics ; 11

ISBN:

9789811002755 [9811002754]    

注記:

Preface -- 1 Bessel Process -- 2 Schramm-Loewner Evolution (SLE) -- 3 Dyson Model -- References -- Solutions -- Index.
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 β is introduced as a multivariate extension of BES(D) with the relation D =

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