Elliptic Determinantal Processes and Elliptic Dyson Models

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 contr...

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Дата:2017
Автор: Katori, M.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2017
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/149273
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Elliptic Determinantal Processes and Elliptic Dyson Models / M. Katori // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 43 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1492732019-02-20T01:23:57Z Elliptic Determinantal Processes and Elliptic Dyson Models Katori, M. 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 AN₋₁, BN, CN and DN, 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. 2017 Article Elliptic Determinantal Processes and Elliptic Dyson Models / M. Katori // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 43 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 60J65; 60G44; 82C22; 60B20; 33E05; 17B22 DOI:10.3842/SIGMA.2017.079 http://dspace.nbuv.gov.ua/handle/123456789/149273 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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 AN₋₁, BN, CN and DN, 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.
format Article
author Katori, M.
spellingShingle Katori, M.
Elliptic Determinantal Processes and Elliptic Dyson Models
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Katori, M.
author_sort Katori, M.
title Elliptic Determinantal Processes and Elliptic Dyson Models
title_short Elliptic Determinantal Processes and Elliptic Dyson Models
title_full Elliptic Determinantal Processes and Elliptic Dyson Models
title_fullStr Elliptic Determinantal Processes and Elliptic Dyson Models
title_full_unstemmed Elliptic Determinantal Processes and Elliptic Dyson Models
title_sort elliptic determinantal processes and elliptic dyson models
publisher Інститут математики НАН України
publishDate 2017
url http://dspace.nbuv.gov.ua/handle/123456789/149273
citation_txt Elliptic Determinantal Processes and Elliptic Dyson Models / M. Katori // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 43 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT katorim ellipticdeterminantalprocessesandellipticdysonmodels
first_indexed 2023-05-20T17:31:27Z
last_indexed 2023-05-20T17:31:27Z
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