Matrix product approach for the asymmetric random average process

Abstract

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.

17 pages, 1 figure

References in corpus (2)

• Broken Ergodicity in a Stochastic Model with Condensation
• Force correlations in the q-model for general q-distributions

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