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This paper deals with the homogenization of the Poisson equation in a boundeddomain of $\mathbb{R}^d$, $d>2$, which is perforated by a random number ofsmall spherical holes with random radii and positions. We show that for a classof stationary short-range correlated measures for the centres and radii of theholes, we recover in the homogenized limit an averaged analogue of the "strangeterm" obtained by Cioranescu and Murat in the periodic case [D. Cioranescu andF. Murat, \textit{Un term \'etrange venu d'ailleurs} (1986)]. We stress that weonly require that the random radii have finite $(d-2)$-moment, which is theminimal assumption in order to ensure that the average of the capacity of theballs is finite. Under this assumption, there are holes which overlap withprobability one. However, we show that homogenization occurs and that theclustering holes do not have any effect in the resulting homogenized equation.

Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes