Quantitative Homogenization of Elliptic PDE with Random Oscillatory   Boundary Data
  We study the averaging behavior of nonlinear uniformly elliptic partial differential equations with random Dirichlet or Neumann boundary data oscillating on a small scale. Under conditions on the operator, the data and the random media leading to concentration of measure, we prove an almost sure and local uniform homogenization result with a rate of convergence in probability. 
William M. Feldman, Inwon Kim, Panagiotis E. Souganidis
math.AP