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Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty }\) kernels

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We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space \(\dot{W}^{-1,\infty }\), thus including the Biot–Savart law and the point vortices dynamics for the 2d incompressible Navier–Stokes.

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  1. Zhenfu Wang

    Present address: Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, USA

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  1. CSCAMM and Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Pierre-Emmanuel Jabin & Zhenfu Wang

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  1. Pierre-Emmanuel Jabin
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Correspondence to Zhenfu Wang.

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P. E. Jabin is partially supported by NSF Grant 1312142 and by NSF Grant RNMS (Ki-Net) 1107444. Z. Wang is partially supported by NSF Grant 1312142 and Ann G. Wylie Dissertation Fellowship.

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Jabin, PE., Wang, Z. Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty }\) kernels. Invent. math. 214, 523–591 (2018). https://doi.org/10.1007/s00222-018-0808-y

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