  In this paper, we propose an offline-online strategy based on the Localized
Orthogonal Decomposition (LOD) method for elliptic multiscale problems with
randomly perturbed diffusion coefficient. We consider a periodic deterministic
coefficient with local defects that occur with probability $p$. The offline
phase pre-computes entries to global LOD stiffness matrices on a single
reference element (exploiting the periodicity) for a selection of defect
configurations. Given a sample of the perturbed diffusion the corresponding LOD
stiffness matrix is then computed by taking linear combinations of the
pre-computed entries, in the online phase. Our computable error estimates show
that this yields a good coarse-scale approximation of the solution for small
$p$. Moreover, extensive numerical experiments illustrate that relative errors
of a few percent are achieved up to at least $p=0.1$. This makes the proposed
technique attractive already for moderate sample sizes in a Monte Carlo
simulation.
