Sample-path large deviation principle for a 2-D stochastic interacting vortex dynamics with singular kernel

Chen, Chenyang; Ge, Hao

doi:10.48550/arxiv.2205.11013

Cited by 1 publication

(1 citation statement)

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“…Very recently, the authors proved the Gaussian fluctuations in [WZZ21] by a tightness argument. We also mention the recent large deviation result obtained by Chen and Ge [CG22]. However, we are not aware of any mean-field approximations to the system of the passive scalar (1.9).…”

Section: Introductionmentioning

confidence: 87%

Mean-field limit of Non-exchangeable interacting diffusions with singular kernels

Wang¹,

Zhao²,

Zhu³

2022

Preprint

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The mean-field limits of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights are mixed, and the interaction kernel has a singularity of the type L q ([0, T ], L p (R d )) for some p, q 1. We demonstrate that the sequence of signed empirical measure processes with arbitary uniform l r -weights, r > 1, weakly converges to a coupled PDE, such as the dynamics describing the passive scalar advected by the 2D Navier-Stokes equation.Our method is based on a tightness/compactness argument and makes use of the systems' uniform Fisher information. The main difficulty is to determine how to propagate the regularity properties of the limits of empirical measures in the absence of the DeFinetti-Hewitt-Savage theorem for the non-exchangeable case. To this end, a sequence of random measures, which merges weakly with a sequence of weighted empirical measures and has uniform Sobolev regularity, is constructed through the disintegration of the joint laws of particles. 1 j N |w N j | = O(1), for r = ∞, as N → ∞, (1.2)where O(•) means "proportional to".

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Section: Introductionmentioning

confidence: 87%