Special Seminar in Applied Mathematics
In this talk I shall address the issue of existence of stationary correctors in stochastic homogenization of linear elliptic equations in divergence form. I shall prove that under the assumption that a spectral gap estimate holds in probability, a stationary corrector exists in dimension larger than 2. I shall also derive various additional estimates on the corrector and on its approximations, including a CLT-like scaling for spatial averages of the energy density of the corrector.
This is joint work with Felix Otto (MPI Leipzig).