Random walks, martingales, and homogenization

I will present probabilistic ideas that arise in relation to homogenization, without assuming familiarity of the audience with probability. We will first see how to define a random walk on a graph, how to relate it to a PDE, and what the homogenization of this PDE means for the random walk. I will then define the concept of a martingale, and give a sketch of proof of homogenization based on this tool.