Homogenization of the random Neumann sieve problem under minimal assumptions on the size of the perforations

We study the limit behavior of the solutions to the Neumann sieve problem for the Poisson equation when the sieve-holes are randomly distributed according to a stationary marked point process. We determine the optimal stochastic integrability for the random radii of the perforations for which stochastic homogenization takes place despite the presence of clustering holes.