Branching Random Walks and Branching Brownian Motion Fundamentals

Understanding how populations evolve across space and time is a foundational challenge in probability and stochastic modeling. This text-based course introduces you to branching random walks and branching Brownian motion, demystifying the core principles of particle systems and spatial branching. You will build a solid theoretical foundation in stochastic processes, learning how individual fitness values and spatial parameters shape particle distributions, genealogical trees, and population frontiers over time. What you'll learn: - Understand foundational probability concepts, basic branching processes, and Galton-Watson trees - Learn the mathematical mechanics governing discrete branching random walks and continuous branching Brownian motions - Analyze the spatial distribution, extreme values, and front propagation of branching particle systems - Apply martingales and stopping times to study survival probabilities and population growth - Explore modern connections between branching systems, partial differential equations, and statistical physics - Practice solving theoretical problems through guided mathematical derivations and written exercises The course begins with fundamental terminology and simple random walks before progressing to continuous spatial branching systems and asymptotic behaviors. It is designed for learners with an interest in probability and stochastic processes, requiring only basic mathematical familiarity. Start reading today to deepen your understanding of spatial branching models.