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SIGMA, 2007, Volume 3, 068, 12 pages (Mi sigma194)  

This article is cited in 2 scientific papers (total in 2 papers)

Hidden Symmetries of Stochastic Models

Boyka Aneva

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria

Abstract: 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.

Keywords: stohastic models; tridiagonal algebra; Askey–Wilson polynomials

DOI: https://doi.org/10.3842/SIGMA.2007.068

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Full text: http://emis.mi.ras.ru/.../068
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Bibliographic databases:

ArXiv: 0705.2671
MSC: 60J60; 17B80
Received: November 23, 2006; in final form May 4, 2007; Published online May 18, 2007
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Citation: Boyka Aneva, “Hidden Symmetries of Stochastic Models”, SIGMA, 3 (2007), 068, 12 pp.

Citation in format AMSBIB
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\by Boyka Aneva
\paper Hidden Symmetries of Stochastic Models
\jour SIGMA
\yr 2007
\vol 3
\papernumber 068
\totalpages 12
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. de Gier, J, “Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries”, Journal of Physics A-Mathematical and Theoretical, 41:48 (2008), 485002  crossref  mathscinet  zmath  isi  scopus
    2. Aneva B., “Boundary Algebra and Exact Solvability of the Asymmetric Exclusion Process”, Journal of Nonlinear Mathematical Physics, 15 (2008), 22–33, Suppl. 3  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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