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Title: Quantitative Homogenization of the Invariant Measure for Nondivergence Form Elliptic Equations

Abstract:

In this talk, I will first give an overview of stochastic homogenization for nondivergence form elliptic equations, and its probabilistic counterpart, the study of quenched invariance principles for nonreversible diffusion processes. I will then present new quantitative homogenization results for the parabolic Green Function (fundamental solution) and for the unique ergodic invariant measure. This invariant measure is a solution of the adjoint equation in doubly divergence form, satisfying certain integrability conditions. I will discuss the implications of these homogenization results, such as heat kernel bounds on the parabolic Green function, regularity results for the adjoint equation, and quantitative ergodicity for the environmental process. This talk is based on joint work with Scott Armstrong and Benjamin Fehrman.

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Zoom link:

Meeting ID: 831 1853 9851

Passcode: 215516