Pf. Arndt et al., STOCHASTIC-MODELS ON A RING AND QUADRATIC ALGEBRAS - THE 3-SPECIES DIFFUSION PROBLEM, Journal of physics. A, mathematical and general, 31(3), 1998, pp. 833-843
The stationary state of a stochastic process on a ring can be expresse
d using traces of monomials of an associative algebra defined by quadr
atic relations. We consider only exclusion processes and restrict the
type of algebras such that one has recurrence relations for traces of
words of different lengths. This is possible only if the rates satisfy
certain compatibility conditions. These conditions are derived and ex
plicit representations of the generators of the quadratic algebras are
given.