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 $SU_q(n)$...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-05-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://www.emis.de/journals/SIGMA/2007/068/ |
| _version_ | 1818933844888256512 |
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| author | Boyka Aneva |
| author_facet | Boyka Aneva |
| author_sort | Boyka Aneva |
| collection | DOAJ |
| 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 $SU_q(n)$ 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 $SU_q(n)$ 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. |
| first_indexed | 2024-12-20T04:54:51Z |
| format | Article |
| id | doaj.art-491ba9644e814c899dff462ebe0e2b0b |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-20T04:54:51Z |
| publishDate | 2007-05-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-491ba9644e814c899dff462ebe0e2b0b2022-12-21T19:52:44ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-05-013068Hidden Symmetries of Stochastic ModelsBoyka AnevaIn 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 $SU_q(n)$ 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 $SU_q(n)$ 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.http://www.emis.de/journals/SIGMA/2007/068/stohastic modelstridiagonal algebraAskey-Wilson polynomials |
| spellingShingle | Boyka Aneva Hidden Symmetries of Stochastic Models Symmetry, Integrability and Geometry: Methods and Applications stohastic models tridiagonal algebra Askey-Wilson polynomials |
| title | 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_short | Hidden Symmetries of Stochastic Models |
| title_sort | hidden symmetries of stochastic models |
| topic | stohastic models tridiagonal algebra Askey-Wilson polynomials |
| url | http://www.emis.de/journals/SIGMA/2007/068/ |
| work_keys_str_mv | AT boykaaneva hiddensymmetriesofstochasticmodels |