Exact soliton-like probability measures for interacting jump processes
Probability
2015-01-29 v1 Statistical Mechanics
Abstract
The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The nonlinearity compensates jumps induced diffusive behavior giving rise to a soliton-like stationary probability density. The soliton velocity and its sharpness both intimately depend on the interaction strength. Below a critical threshold of the strength of interactions, the cooperative behavior cannot be sustained leading to the destruction of the soliton-like solution. The bifurcation point for this behavioral phase transition is explicitly calculated.
Cite
@article{arxiv.1501.07061,
title = {Exact soliton-like probability measures for interacting jump processes},
author = {Max-Olivier Hongler},
journal= {arXiv preprint arXiv:1501.07061},
year = {2015}
}