Asymmetric Random Average Process: Aggregation and Fragmentation on Continuous State Space
A simple analytically treatable stochastic process on continuous state space, the asymmetric random average process, with a broad range of applications in traffic flow theory, internet modeling and granular media is presented. We concentrate mainly on the analysis of the basic properties of the model. The set of all exact mean field solutions is determined and we point out that it represents a class of very good approximants even for non-product-measure processes. Furthermore we study a truncated process that shows the occurence of a nonsymmetric ergodicity breaking in the thermodynamic limit. This interesting phenomenon shows similar properties as spontaneous symmetry breaking, but without any explicit symmetry.
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