## Quantitative stochastic homogenization of linear elliptic PDE

### Scott Armstrong

Courant Institute of Mathematical Sciences

I will discuss the large-scale asymptotics of solutions of linear elliptic equations with random coefficients. It is well-known that solutions converge (in the limit of scale separation) to those of a deterministic equation, a kind of law of large numbers result called "homogenization". In recent years obtaining quantitative information about this convergence has attracted a lot of attention, which lead to the development of new tools from analysis and probability. I will give an overview of one such approach to the topic based on variational methods, elliptic regularity, and ``renormalization-group'' arguments.