Hidden Symmetries of Stochastic Models

In the matrix product states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a SUq(n) quan...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2007
Автор: Aneva, B.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2007
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147371
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Hidden Symmetries of Stochastic Models / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 30 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147371
record_format dspace
spelling Aneva, B.
2019-02-14T14:48:03Z
2019-02-14T14:48:03Z
2007
Hidden Symmetries of Stochastic Models / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 30 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 60J60; 17B80
https://nasplib.isofts.kiev.ua/handle/123456789/147371
In the matrix product states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a SUq(n) quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the SUq(n) symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). The author would like to thank the organizers for the invitation to participate the O’Raifeartaigh symposium and for the warm and friendly atmosphere during the stay in Budapest.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Hidden Symmetries of Stochastic Models
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Hidden Symmetries of Stochastic Models
spellingShingle Hidden Symmetries of Stochastic Models
Aneva, B.
title_short Hidden Symmetries of Stochastic Models
title_full Hidden Symmetries of Stochastic Models
title_fullStr Hidden Symmetries of Stochastic Models
title_full_unstemmed Hidden Symmetries of Stochastic Models
title_sort hidden symmetries of stochastic models
author Aneva, B.
author_facet Aneva, B.
publishDate 2007
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In the matrix product states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a SUq(n) quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the SUq(n) symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147371
fulltext
citation_txt Hidden Symmetries of Stochastic Models / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 30 назв. — англ.
work_keys_str_mv AT anevab hiddensymmetriesofstochasticmodels
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last_indexed 2025-11-24T06:31:13Z
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