The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an

This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potentia

The only comprehensive guide to modeling, characterizing, and solving partial differential equations This classic text by Erich Zauderer provides a comprehensiv

Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.

The Heat Equation