These lecture notes discuss several related features of the exactly solvable two-dimensional
corner growth model with exponentially distributed weights. A key property of this model is …

arXiv:1512.06375v2 [math.AP] 7 Sep 2016 Page 1 arXiv:1512.06375v2 [math.AP] 7 Sep 2016
Stochastic homogenization of nonconvex Hamilton-Jacobi equations: a counterexample Bruno …

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 present a proof of qualitative stochastic homogenization for a nonconvex Hamilton–
Jacobi equations. The new idea is to introduce a family of “sub-equations” and to control …

We study the ergodic theory of stationary directed nearest-neighbor polymer models on Z^ 2
Z 2, with iid weights. Such models are equivalent to specifying a stationary distribution on …

We prove a shape theorem and derive a variational formula for the limiting quenched
Lyapunov exponent and the Green's function of random walk in a random potential on a …

We consider a finite horizon stochastic optimal control problem for nearest-neighbor random
walk {X_i\} on the set of integers. The cost function is the expectation of the exponential of …

We prove homogenization for a class of viscous Hamilton-Jacobi equations in the stationary
& ergodic setting in one space dimension. Our assumptions include most notably the …

We establish a variational formula for the exponential decay rate of the Green function of
Brownian motion evolving in a random stationary and ergodic nonnegative potential. Such a …

The paper deals with a Dirichlet spectral problem for a singularly perturbed second order
elliptic operator with rapidly oscillating locally periodic coefficients. We study the limit …