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Titlebook: Elliptic Extensions in Statistical and Stochastic Systems; Makoto Katori Book 2023 The Author(s), under exclusive license to Springer Natu

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发表于 2025-3-21 18:45:08 | 显示全部楼层 |阅读模式
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Titlebook: Elliptic Extensions in Statistical and Stochastic Systems;  Makoto Katori Book 2023 The Author(s), under exclusive license to Springer Natu
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
doihttps://doi.org/10.1007/978-981-19-9527-9
isbn_softcover978-981-19-9526-2
isbn_ebook978-981-19-9527-9Series ISSN 2197-1757 Series E-ISSN 2197-1765
issn_series 2197-1757
copyrightThe Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
The information of publication is updating

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发表于 2025-3-21 21:32:00 | 显示全部楼层
https://doi.org/10.1007/978-3-662-44877-9rmer systems, the key aspect of future direction will be dynamical property of DPPs. For the latter systems, it will be the connections to other statistical systems such as the one-component plasma models and the Gaussian free fields.
发表于 2025-3-22 01:49:27 | 显示全部楼层
https://doi.org/10.1007/978-3-322-93175-7of the boundary points and hence we obtain four types of Brownian motion in the interval. We see an interesting correspondence between these four types of Brownian motion and the four types of Jacobi’s theta functions via expressions of the transition probability densities.
发表于 2025-3-22 07:30:40 | 显示全部楼层
发表于 2025-3-22 09:45:20 | 显示全部楼层
Grundlagen der Integralrechnung,e three types of infinite DPPs on .. One of them is the uniform DPP on ., which is identified with the Ginibre DPP well-studied in random matrix theory. The other two DPPs are new, and are rotationally invariant but inhomogeneous in the radial direction.
发表于 2025-3-22 13:03:52 | 显示全部楼层
Brownian Motion and Theta Functions,of the boundary points and hence we obtain four types of Brownian motion in the interval. We see an interesting correspondence between these four types of Brownian motion and the four types of Jacobi’s theta functions via expressions of the transition probability densities.
发表于 2025-3-22 18:12:11 | 显示全部楼层
Biorthogonal Systems of Theta Functions and Macdonald Denominators,give a brief review of the theory of Rosengren and Schlosser. Then we introduce appropriate inner products and prove the biorthogonality relations for the . theta functions of Rosengren and Schlosser.
发表于 2025-3-23 00:20:04 | 显示全部楼层
Doubly Periodic Determinantal Point Processes,e three types of infinite DPPs on .. One of them is the uniform DPP on ., which is identified with the Ginibre DPP well-studied in random matrix theory. The other two DPPs are new, and are rotationally invariant but inhomogeneous in the radial direction.
发表于 2025-3-23 03:03:58 | 显示全部楼层
发表于 2025-3-23 07:46:55 | 显示全部楼层
Future Problems,rmer systems, the key aspect of future direction will be dynamical property of DPPs. For the latter systems, it will be the connections to other statistical systems such as the one-component plasma models and the Gaussian free fields.
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