Exact soliton-like probability measures for interacting jump processes

Max-Olivier Hongler

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arXiv · 1501.07061

Exact soliton-like probability measures for interacting jump processes

Max-Olivier Hongler

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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.

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Max-Olivier Hongler. 2015-01-28. Exact soliton-like probability measures for interacting jump processes. https://arxiv.org/abs/1501.07061

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