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@article{Noronha:2018:10.1007/s00332-017-9433-y,
author = {Noronha, Moreira Antunes Gomes ST and Pavliotis, GA},
doi = {10.1007/s00332-017-9433-y},
journal = {Journal of Nonlinear Science},
pages = {905--941},
title = {Mean field limits for interacting diffusions in a two-scale potential},
url = {http://dx.doi.org/10.1007/s00332-017-9433-y},
volume = {28},
year = {2018}
}

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TY  - JOUR
AB  - In this paper we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic  confining potential, of the form considered in [13]. We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.
AU  - Noronha,Moreira Antunes Gomes ST
AU  - Pavliotis,GA
DO  - 10.1007/s00332-017-9433-y
EP  - 941
PY  - 2018///
SN  - 0938-8974
SP  - 905
TI  - Mean field limits for interacting diffusions in a two-scale potential
T2  - Journal of Nonlinear Science
UR  - http://dx.doi.org/10.1007/s00332-017-9433-y
UR  - http://hdl.handle.net/10044/1/54615
VL  - 28
ER  -

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Professor Grigorios A. Pavliotis

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