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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@article{CRMATH_2022__360_G8_909_0,
author = {Duerinckx, Mitia and Gloria, Antoine},
title = {A short proof of {Gevrey} regularity for homogenized coefficients of the {Poisson} point process},
journal = {Comptes Rendus. Math\'ematique},
pages = {909--918},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
number = {G8},
year = {2022},
doi = {10.5802/crmath.354},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/crmath.354/}
}
TY - JOUR AU - Duerinckx, Mitia AU - Gloria, Antoine TI - A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process JO - Comptes Rendus. Mathématique PY - 2022 SP - 909 EP - 918 VL - 360 IS - G8 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.354/ DO - 10.5802/crmath.354 LA - en ID - CRMATH_2022__360_G8_909_0 ER -
%0 Journal Article %A Duerinckx, Mitia %A Gloria, Antoine %T A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process %J Comptes Rendus. Mathématique %D 2022 %P 909-918 %V 360 %N G8 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.354/ %R 10.5802/crmath.354 %G en %F CRMATH_2022__360_G8_909_0
Duerinckx, Mitia; Gloria, Antoine. A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 909-918. doi : 10.5802/crmath.354. http://archive.numdam.org/articles/10.5802/crmath.354/
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