Diffusion algebras

Abstract

We define the notion of "diffusion algebras". They are quadratic\nPoincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact\nexpressions for the probability distributions of stationary states appearing in\none-dimensional stochastic processes with exclusion. One considers processes in\nwhich one has N species, the number of particles of each species being\nconserved. All diffusion algebras are obtained. The known examples already used\nin applications are special cases in our classification. To help the reader\ninterested in physical problems, the cases N=3 and 4 are listed separately.\n