Hidden Symmetries of Stochastic Models
Abstract
In the matrix product states approach to 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 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 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.
Cite
@article{arxiv.0705.2671,
title = {Hidden Symmetries of Stochastic Models},
author = {Boyka Aneva},
journal= {arXiv preprint arXiv:0705.2671},
year = {2008}
}