Probabilistic Dynamics on Large Graphs

This advanced topics course studies probabilistic models of large graphs and stochastic processes evolving on them, following Rick Durrett’s Dynamics on Graphs. The course develops rigorous tools from probability theory to analyze random graph models, interacting particle systems, and network-based stochastic dynamics. Topics include Erdős–Rényi and related random graph models, branching process and exploration techniques, phase transitions, and scaling limits, as well as dynamic processes on graphs such as epidemic models, contact processes, and voter-type systems. Emphasis is placed on asymptotic analysis, coupling arguments, and mean-field and high-dimensional methods that are central to current research in probability. The course is intended for advanced graduate students with a strong background in measure-theoretic probability and stochastic processes.