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This article is cited in 4 scientific papers (total in 4 papers)
Elliptic Determinantal Processes and Elliptic Dyson Models
Makoto Katori Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
Abstract:
We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families ${A}_{N-1}$, ${B}_N$, ${C}_N$ and ${D}_N$, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser.
Keywords:
elliptic determinantal processes; elliptic Dyson models; determinantal martingales; elliptic determinant evaluations; irreducible reduced affine root systems.
Received: April 19, 2017; in final form September 29, 2017; Published online October 4, 2017
Citation:
Makoto Katori, “Elliptic Determinantal Processes and Elliptic Dyson Models”, SIGMA, 13 (2017), 079, 36 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1279 https://www.mathnet.ru/eng/sigma/v13/p79
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Abstract page: | 121 | Full-text PDF : | 31 | References: | 25 |
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