Kavita Ramanan - Interacting Stochastic Processes on Sparse Random Graphs
Explore a 50-minute lecture on interacting stochastic processes on sparse random graphs, delivered by Kavita Ramanan for the International Mathematical Union. Delve into recent progress in characterizing hydrodynamic limits and marginal dynamics of stochastic processes on sparse random interaction graphs. Compare their behavior with classically studied mean-field limits arising from complete interaction graphs. Examine applications in statistical physics, neuroscience, biology, and engineering. Learn about local weak convergence of graphs, process convergence results, and global empirical measure convergence. Investigate marginal dynamics on various graph structures, including infinite d-regular trees and unimodular Galton-Watson trees. Discover analogous convergence results for jump processes and explore Markovian approximations for detecting phase transitions and analyzing transient behavior.