Mean-field limit versus small-noise limit for some interacting particle systems
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.
Cite
@article{arxiv.1409.1159,
title = {Mean-field limit versus small-noise limit for some interacting particle systems},
author = {Samuel Herrmann and Julian Tugaut},
journal= {arXiv preprint arXiv:1409.1159},
year = {2014}
}