{"product_id":"9789811002748","title":"SpringerBriefs in Mathematical Physics","description":"\u003ch1\u003eSpringerBriefs in Mathematical Physics\u003c\/h1\u003e \u003ch2\u003eKatori, Makoto\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThe 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 \u003ci\u003eD\u003c\/i\u003e, BES(\u003ci\u003eD\u003c\/i\u003e), 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(\u003ci\u003eD\u003c\/i\u003e) is defined for any \u003ci\u003eD\u003c\/i\u003e ≥ 1. Dependence of the BES(\u003ci\u003eD\u003c\/i\u003e) path on its initial value is represented by the Bessel flow. In Chap. 2 SLE is introduced as a complexification of BES(\u003ci\u003eD\u003c\/i\u003e). Rich mathematics and physics involved in SLE are due to the nontrivial dependence of the Bessel flow on \u003ci\u003eD\u003c\/i\u003e. 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(\u003ci\u003eD\u003c\/i\u003e) with the relation \u003ci\u003eD\u003c\/i\u003e = β + 1. The book concentrates on the case where β = 2 and calls this case simply the Dyson model.\u003c\/div\u003e\u003cdiv\u003eThe 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. \u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2016-02-16\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811002748\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-10-0275-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 141\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":46547628064908,"sku":"9789811002748","price":58.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811002748.jpg?v=1775835678","url":"https:\/\/lateknightbooks.com\/products\/9789811002748","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}