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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2017
Автор: Katori, M.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2017
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/149273
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
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.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862713671237500928
author Katori, M.
author_facet Katori, M.
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
first_indexed 2025-12-07T17:45:57Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-149273
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T17:45:57Z
publishDate 2017
publisher Інститут математики НАН України
record_format dspace
spelling Katori, M.
2019-02-19T19:40:23Z
2019-02-19T19:40:23Z
2017
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
https://nasplib.isofts.kiev.ua/handle/123456789/149273
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.
This paper is a contribution to the Special Issue on Elliptic Hypergeometric Functions and Their Applications.
 The full collection is available at https://www.emis.de/journals/SIGMA/EHF2017.html.
 The author would like to thank the anonymous referees whose comments considerably improved
 the presentation of the paper. A part of the present work was done during the participation of
 the author in the ESI workshop on “Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics” (March 20–24, 2017). The present author expresses his gratitude
 for the hospitality of Erwin Schr¨odinger International Institute for Mathematics and Physics
 (ESI) of the University of Vienna and for well-organization of the workshop by Christian Krattenthaler, Masatoshi Noumi, Simon Ruijsenaars, Michael J. Schlosser, Vyacheslav P. Spiridonov,
 and S. Ole Warnaar. He also thanks Soichi Okada, Masatoshi Noumi, Simon Ruijsenaars, and
 Michael J. Schlosser for useful discussion. This work was supported in part by the Grant-in-Aid
 for Scientific Research (C) (No. 26400405), (B) (No. 26287019), and (S) (No. 16H06338) of
 Japan Society for the Promotion of Science.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Elliptic Determinantal Processes and Elliptic Dyson Models
Article
published earlier
spellingShingle Elliptic Determinantal Processes and Elliptic Dyson Models
Katori, M.
title 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_short Elliptic Determinantal Processes and Elliptic Dyson Models
title_sort elliptic determinantal processes and elliptic dyson models
url https://nasplib.isofts.kiev.ua/handle/123456789/149273
work_keys_str_mv AT katorim ellipticdeterminantalprocessesandellipticdysonmodels