| 期刊全稱 | Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model | | 影響因子2023 | Makoto Katori | | 視頻video | http://file.papertrans.cn/185/184180/184180.mp4 | | 發(fā)行地址 | 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 ran | | 學科分類 | SpringerBriefs in Mathematical Physics | | 圖書封面 |  | | 影響因子 | 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. =?β?+ 1. The book concentrates on the case where?β?= 2 and calls this case simply the Dyson model..The Dyson model inherits the two aspects of BES(3); hence it | | Pindex | Book 2016 |
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