Introduction to Fronts in Random Media

The aim of this book is to give a user friendly tutorial of an interdisciplinary research topic (fronts in random media) to senior undergraduates and beginning graduate students with basic knowledge of partial differential equations (PDE) and probability. The approach taken is semi-formal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigorous theorems with details found in references of the bibliography. As the topic concerns both differential equations and probability, yet probability is traditionally a technical subject with heavy measure theoretical treatment, the book strives to develop a simplistic approach so students can grasp the essentials of fronts and random media and their applications in a self-contained tutorial. The scope of the book goes from wave properties of scalar deterministic PDEs (Burgers, Hamilton-Jacobi, reaction-diffusion etc.) to the asymptotic analysis of their stochastic versions.