Mean-field limit versus small-noise limit for some interacting particle systems

Samuel Herrmann; Julian Tugaut

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arXiv · 1409.1159

Mean-field limit versus small-noise limit for some interacting particle systems

Samuel Herrmann·Julian Tugaut

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Abstract

In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes. Such diffusions can be obtained by taking the hydrodymamic limit in a huge system of linear diffusions in interaction. In both cases, for the linear and the nonlinear processes, small-noise asymptotics have been emphasized by specific large deviation phenomenons. The natural question, therefore, is: is it possible to interchange the mean-field limit with the small-noise limit? The aim here is to consider this question by proving that the rate function of the first particle in a mean-field system converges to the rate function of the hydrodynamic limit as the number of particles becomes large.

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Samuel Herrmann, Julian Tugaut. 2014-09-03. Mean-field limit versus small-noise limit for some interacting particle systems. https://arxiv.org/abs/1409.1159

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