Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

Details Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

1997-03-20

arxiv.org/abs/cond-mat/9703182v2

J.Phys.A:Math.Gen. 31 (1998) 833

Physics

Condensed Matter

Statistical Mechanics

12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.A

Scientific paper

10.1088/0305-4470/31/3/003

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.

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