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In this short note we capitalize on and complete our previous results on theregularity of the homogenized coefficients for Bernoulli perturbations byaddressing the case of the Poisson point process, for which the crucial uniformlocal finiteness assumption fails. In particular, we strengthen the qualitativeregularity result first obtained in this setting by the first author to Gevreyregularity of order~2. The new ingredient is the independence of Poisson pointprocesses, in a form recently used by Giunti, Gu, Mourrat, and Nitzschner.

A short proof of Gevrey regularity for homogenized coefficients of the Poisson point process