2001/03/31 by A. P. Isaev, P. N. Pyatov, Pavel Pyatov +1 · 3 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math.QA
paper · pdf · doi:10.1088/0305-4470/34/29/306
29 pages; minor misprints corrected, few references added
arxiv created 2001/06/07 · openalex publication_date 2001/07/16 · arxiv updated 2009/11/30 · openalex created_date 2020/07/02 · openalex updated_date 2026/07/28
We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) 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.