2009/02/28 by Farhad H Jafarpour, F. H. Jafarpour, S. R. Masharian · 1 citation
Mathematics · Physics and Astronomy · #Asymmetric simple exclusion process #Bernoulli's principle #Equivalence (formal languages) #Lattice (music) #Markov Chains and Monte Carlo Methods #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Physics #Product (mathematics) #Pure mathematics #Quadratic equation #Random walk #Representation (politics) #Simple (philosophy) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.051124
published as Phys. Rev. E 79, 051124 (2009) · 5 pages, reference added, minor revision
openalex publication_date 2009/05/22 · arxiv created 2009/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is known that when the steady state of a one-dimensional multispecies system, which evolves via a random-sequential updating mechanism, is written in terms of a linear combination of Bernoulli shock measures with random-walk dynamics, it can be equivalently expressed as a matrix-product state. In this case the quadratic algebra of the system always has a two-dimensional matrix representation. Our investigations show that this equivalence exists at least for the systems with deterministic sublattice-parallel update. In this paper we consider the totally asymmetric simple exclusion process on a finite lattice with open boundaries and sublattice-parallel update as an example.