Pré-Publication, Document De Travail Année : 2025

Propagation of chaos in Fisher information

Résumé

We present a new method for proving sharp local propagation of chaos in Fisher Information for particles with smooth interaction and drift. We rely on a new Lemma computing the Fisher Information of two diffusion processes with smooth drifts and fine estimates on the hessian of the law of the solution of the McKean-Vlasov equation. It allows us to obtain a new propagation of chaos in Fisher information, generalizing Lacker's seminal work by using the BBGKY hierarchy to obtain a system of differential inequalities satisfied by both the relative entropy and the Fisher Information of k particles. We also show with a simple Gaussian example that our decay rate is optimal.

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Dates et versions

hal-05379873 , version 1 (24-11-2025)

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  • HAL Id : hal-05379873 , version 1

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Jules Grass, Christophe Poquet, Arnaud Guillin. Propagation of chaos in Fisher information. 2025. ⟨hal-05379873⟩
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