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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Hidden Symmetries of Stochastic Models
Boyka Aneva Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria
Аннотация:
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.
Ключевые слова:
stohastic models; tridiagonal algebra; Askey–Wilson polynomials.
Поступила: 23 ноября 2006 г.; в окончательном варианте 4 мая 2007 г.; опубликована 18 мая 2007 г.
Образец цитирования:
Boyka Aneva, “Hidden Symmetries of Stochastic Models”, SIGMA, 3 (2007), 068, 12 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma194 https://www.mathnet.ru/rus/sigma/v3/p68
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