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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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147371 |
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dspace |
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irk-123456789-1473712019-02-15T01:25:12Z Hidden Symmetries of Stochastic Models Aneva, B. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147371 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 |
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. |
| format |
Article |
| author |
Aneva, B. |
| spellingShingle |
Aneva, B. Hidden Symmetries of Stochastic Models Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Aneva, B. |
| author_sort |
Aneva, B. |
| title |
Hidden Symmetries of Stochastic Models |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147371 |
| citation_txt |
Hidden Symmetries of Stochastic Models / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 30 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT anevab hiddensymmetriesofstochasticmodels |
| first_indexed |
2023-05-20T17:27:17Z |
| last_indexed |
2023-05-20T17:27:17Z |
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1796153329255972864 |