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A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process
Mitia Duerinckx1 ; Antoine Gloria2
1 Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France & Université Libre de Bruxelles, Département de Mathématique, 1050 Brussels, Belgium
2 Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions, 75005 Paris, France & Institut Universitaire de France & Université Libre de Bruxelles, Département de Mathématique, 1050 Brussels, Belgium
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 909-918.

In this short note we capitalize on and complete our previous results on the regularity of the homogenized coefficients for Bernoulli perturbations by addressing the case of the Poisson point process, for which the crucial uniform local finiteness assumption fails. In particular, we strengthen the qualitative regularity result first obtained in this setting by the first author to Gevrey regularity of order 2. The new ingredient is a fine application of properties of Poisson point processes, in a form recently used by Giunti, Gu, Mourrat, and Nitzschner.

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Accepté le :
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DOI : 10.5802/crmath.354
Classification : 35R60, 60G55

Mitia Duerinckx 1 ; Antoine Gloria 2

1 Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France & Université Libre de Bruxelles, Département de Mathématique, 1050 Brussels, Belgium
2 Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions, 75005 Paris, France & Institut Universitaire de France & Université Libre de Bruxelles, Département de Mathématique, 1050 Brussels, Belgium
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Comptes Rendus. Math\'ematique},
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Mitia Duerinckx; Antoine Gloria. A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 909-918. doi : 10.5802/crmath.354. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.354/

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