RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 SIGMA: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (219 kB)
Full text: http://emis.mi.ras.ru/.../068
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 0705.2671
MSC: 60J60; 17B80
Received: November 23, 2006; in final form May 4, 2007; Published online May 18, 2007
Language:

Citation: Boyka Aneva, “Hidden Symmetries of Stochastic Models”, SIGMA, 3 (2007), 068, 12 pp.

Citation in format AMSBIB
\Bibitem{Ane07} \by Boyka Aneva \paper Hidden Symmetries of Stochastic Models \jour SIGMA \yr 2007 \vol 3 \papernumber 068 \totalpages 12 \mathnet{http://mi.mathnet.ru/sigma194} \crossref{https://doi.org/10.3842/SIGMA.2007.068} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2322795} \zmath{https://zbmath.org/?q=an:1158.60035} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000207065200068} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889236642} 

• http://mi.mathnet.ru/eng/sigma194
• http://mi.mathnet.ru/eng/sigma/v3/p68

 SHARE:

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
2. Aneva B., “Boundary Algebra and Exact Solvability of the Asymmetric Exclusion Process”, Journal of Nonlinear Mathematical Physics, 15 (2008), 22–33, Suppl. 3
•  Number of views: This page: 124 Full text: 17 References: 11