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

Peter F. Arndt·Thomas Heinzel·Vladimir Rittenberg
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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.

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Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg. 1997-05-19. Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem. https://doi.org/10.1088/0305-4470%2F31%2F3%2F003

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