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We consider a homogenization problem for the diffusion equation$-\operatorname{div}\left(a_{\varepsilon} \nabla u_{\varepsilon} \right) = f$when the coefficient $a_{\varepsilon}$ is a non-local perturbation of aperiodic coefficient. The perturbation does not vanish but becomes rare atinfinity in a sense made precise in the text. We prove the existence of acorrector, identify the homogenized limit and study the convergence rates of$u_{\varepsilon}$ to its homogenized limit.

A periodic homogenization problem with defects rare at infinity