Explore interacting stochastic processes on random graphs in this AAAS-AMS Invited Address from the 2022 Virtual Joint Mathematics Meetings. Delve into discrete time contact processes, continuous time models, voter models, and spike train models. Examine neuronal hox models, coupled oscillators, and the evolution of stochastic processes. Investigate classical limit theorems, weak convergence, empirical measures, and Wiener measure. Analyze weak interactions in dense graphs and sparse regimes, addressing challenges and counterexamples. Study local convergence, autonomous characterization, and unimodular roots in discrete time processes.
Overview
Syllabus
Introduction
Kavita Ramanan
About this talk
Discrete time contact process
continuous time models
voter model
spike train model
neuronal hox model
coupled oscillators
stochastic processes evolving
questions of interest
classical limit theorems
weak convergence
empirical measures
Wiener measure
Weak interactions
Dense graphs
Sparse regime
Challenges in sparse regime
Local convergence
Counterexamples
Autonomous characterization
Unimodular roots
Discrete time process
Goal
Taught by
Joint Mathematics Meetings
