Branching Random Walks and Brownian Motion Fundamentals

Understanding how particles spread and reproduce simultaneously is a central problem in probability theory and stochastic analysis. This course provides a clear, step-by-step introduction to the mathematics of branching random walks and branching Brownian motion. What you will learn: Understand the core definitions of branching processes, discrete random walks, and spatial particle systems; Analyze wavefront propagation and reaction-diffusion models using the KPP framework; Apply first and second moment methods alongside change-of-measure techniques; Evaluate extreme values and the asymptotic behavior of maximal particles; Connect theoretical probability models with modern computational verification and analytical recursions. You will begin with essential terminology and elementary branching trees before advancing to continuous diffusion models and asymptotic properties. This course is written for learners with basic familiarity with probability and calculus who want an accessible, self-paced mathematical introduction without advanced prerequisites. Begin reading today to master the mechanics of spatial branching processes.