  This work is devoted to the asymptotic behavior of eigenvalues of an elliptic
operator with rapidly oscillating random coefficients on a bounded domain with
Dirichlet boundary conditions. A sharp convergence rate is obtained for
isolated eigenvalues towards eigenvalues of the homogenized problem, as well as
a quantitative two-scale expansion result for eigenfunctions. Next, a
quantitative central limit theorem is established for eigenvalue fluctuations;
more precisely, a pathwise characterization of eigenvalue fluctuations is
obtained in terms of the so-called homogenization commutator, in parallel with
the recent fluctuation theory for the solution operator.
