Abstract
The paper deals with the singularly perturbed Dirichlet problem in a randomly perforated domain Ωε in RN. The domain Ωε is obtained from a bounded open set Ω after removing approximately mε−q small holes, whose size is of order εp (N>3) and exp, randomly according to a probability density function . The L2(Ω) limit of uε in probability in the space of configurations of holes when ε→0, which depends on p and q, is derived. An order of convergence can also be deduced (with regularity assumptions for f). Results on the fluctuation of the volume of the Wiener sausage and the long time asymptotics of the shrinking Wiener sausage together with the Feynman-Kac formula are the main tools of analysis.
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