Matrix product approach for the asymmetric random average process

Details Matrix product approach for the asymmetric random average process Matrix product approach for the asymmetric random average process

2002-11-21

arxiv.org/abs/cond-mat/0211472v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 1 figure

Scientific paper

10.1088/0305-4470/36/13/306

We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called beta densities, of all local interactions leading to steady states of product measure form are rigorously derived. This also completes an outstanding proof given in a previous publication. Then, we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz. Due to continuous state variables we obtain a matrix algebra in form of a functional equation which can be solved exactly.

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