  $\Gamma$-convergence methods are used to prove homogenization results for
fractional obstacle problems in periodically perforated domains. The obstacles
have random sizes and shapes and their capacity scales according to a
stationary ergodic process. We use a trace-like representation of fractional
Sobolev norms in terms of weighted Sobolev energies established by Caffarelli
and Silvestre, a weighted ergodic theorem and a joining lemma in varying
domains following the approach by Ansini and Braides.
  Our proof is alternative to those contained in the papers by Caffarelli and
Mellet.

Classical Analysis and ODEs