书目名称 | Elliptic Extensions in Statistical and Stochastic Systems | 编辑 | Makoto Katori | 视频video | | 概述 | Explains elliptic extensions using the Brownian motion and determinantal point processes.Uses only one kind of special function, called the theta function, and visualizes elliptic extensions using gra | 丛书名称 | SpringerBriefs in Mathematical Physics | 图书封面 |  | 描述 | Hermite‘s theorem makes it known that there are three levels of mathematical frames in which a simple addition formula is valid. They are rational, q-analogue, and elliptic-analogue. Based on the addition formula and associated mathematical structures, productive studies have been carried out in the process of .q.-extension of the rational (classical) formulas in enumerative combinatorics, theory of special functions, representation theory, study of integrable systems, and so on. Originating from the paper by Date, Jimbo, Kuniba, Miwa, and Okado on the exactly solvable statistical mechanics models using the theta function identities (1987), the formulas obtained at the .q.-level are now extended to the elliptic level in many research fields in mathematics and theoretical physics. In the present monograph, the recent progress of the elliptic extensions in the study of statistical and stochastic models in equilibrium and nonequilibrium statistical mechanics and probability theory is shown. At the elliptic level, many special functions are used, including Jacobi‘s theta functions, Weierstrass elliptic functions, Jacobi‘s elliptic functions, and others. This monograph is not intended t | 出版日期 | Book 2023 | 关键词 | q-extensions and elliptic extensions; Probability theory and stochastic processes; Statistical physics | 版次 | 1 | doi | https://doi.org/10.1007/978-981-19-9527-9 | isbn_softcover | 978-981-19-9526-2 | isbn_ebook | 978-981-19-9527-9Series ISSN 2197-1757 Series E-ISSN 2197-1765 | issn_series | 2197-1757 | copyright | The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 |
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