Hidden Symmetries of Stochastic Models

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dc.creatorAneva, Boyka
dc.date2007-05-18
dc.date.accessioned2026-07-07T09:34:06Z
dc.date.available2026-07-07T09:34:06Z
dc.descriptionIn 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.
dc.descriptionThis is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/0705.2671
dc.identifierhttp://arxiv.org/abs/0705.2671
dc.identifierSIGMA 3 (2007), 068, 12 pages
dc.identifierdoi:10.3842/SIGMA.2007.068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159371
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleHidden Symmetries of Stochastic Models
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