Diffusion algebras
- 16 July 2001
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 34 (29), 5815-5834
- https://doi.org/10.1088/0305-4470/34/29/306
Abstract
We define the notion of `diffusion algebras'. They are quadratic Poincaré-Birkhoff-Witt algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional stochastic processes with exclusion. One considers processes in which one has N species, the number of particles of each species being conserved. All diffusion algebras are obtained. The known examples already used in applications are special cases in our classification. To help the reader interested in physical problems, the cases N = 3 and 4 are listed separately.Keywords
Other Versions
This publication has 24 references indexed in Scilit:
- Multispecies asymmetric simple exclusion process and its relation to traffic flowPhysical Review E, 1999
- Stochastic models of interacting systemsThe Annals of Probability, 1997
- Representations of the quadratic algebra and partially asymmetric diffusion with open boundariesJournal of Physics A: General Physics, 1996
- Exact solution of the totally asymmetric simple exclusion process: Shock profilesJournal of Statistical Physics, 1993
- Phase transitions in an exactly soluble one-dimensional exclusion processJournal of Statistical Physics, 1993
- A remark on quasi-triangular Lie algebrasPhysics Letters B, 1991
- The quantum group structure associated with non-linearly extended Virasoro algebrasCommunications in Mathematical Physics, 1990
- Multiparametric quantum deformation of the general linear supergroupCommunications in Mathematical Physics, 1989
- The diamond lemma for ring theoryAdvances in Mathematics, 1978
- Treue Darstellung Liescher Ringe.Journal für die reine und angewandte Mathematik (Crelles Journal), 1937