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Hidden Symmetries of Stochastic Models
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Hidden Symmetries of Stochastic Models
Інший ID:
2000 Mathematics Subject Classification: 60J60; 17B80
Посилання:
Hidden Symmetries of Stochastic Models / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 30 назв. — англ.
Підтримка:
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.
Дата:
2007
Переглядів:
494
Завантажень:
255
Анотація:
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.
