This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

We consider a first-order system of mean field games with local coupling in the deterministic
limit. Under general structure conditions on the Hamiltonian and coupling, we prove …

This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or
interfaces in random media) to senior undergraduates and beginning grad uate students …

We establish a logarithmic-type rate of convergence for the homogenization of fully
nonlinear uniformly elliptic second-order pde in strongly mixing media with similar, ie …

We study quenched distributions on random walks in a random potential on integer lattices
of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can …

We consider the homogenization of Hamilton–Jacobi equations and degenerate Bellman
equations in stationary, ergodic, unbounded environments. We prove that, as the …

We present a simple, new proof for the stochastic homogenization of quasiconvex (level-set
convex) Hamilton–Jacobi equations set in stationary ergodic environments. Our approach …

The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian
motion with a linear drift as a stationary distribution (modulo additive constants). We show …

We discuss variational formulas for the law of large numbers limits of certain models of
motion in a random medium: namely, the limiting time constant for last-passage percolation …

We consider a random walk in a random potential on a square lattice of arbitrary dimension.
The potential is a function of an ergodic environment and steps of the walk. The potential is …