Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
Statistical Mechanics
2009-10-30 v2
Abstract
The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras.
Keywords
Cite
@article{arxiv.cond-mat/9703182,
title = {Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem},
author = {Peter F. Arndt and Thomas Heinzel and Vladimir Rittenberg},
journal= {arXiv preprint arXiv:cond-mat/9703182},
year = {2009}
}
Comments
12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.A