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Kavita Ramanan - Interacting Stochastic Processes on Sparse Random Graphs
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- 1 Intro
- 2 Interacting Stochastic Processes
- 3 A Prototype Examples Pairwise Interacting Diffusions
- 4 Global Empirical Measure Process
- 5 Key Questions
- 6 Outline of the Rest of the Talk
- 7 Classical Mean-Field Results for Interacting Diffusions
- 8 Summary of the Classical Case
- 9 Challenges in the Sparse Regime
- 10 Local weak convergence of graphs
- 11 Local convergence of marked graphs
- 12 Examples of local weak convergence of deterministic graphs
- 13 Modes of Local Convergence for Random Graph Sequences
- 14 Other Examples of Local weak convergence of random graphs
- 15 A More General Class of Interacting Diffusions
- 16 1. Process Convergence Results
- 17 Global Empirical Measure Convergence Results
- 18 2. Global Empirical Measure Convergence
- 19 Marginal Dynamics on the Line
- 20 Key Properties of the Marginal Dynamics/Local Equations
- 21 Elements of the Proof: 1. A Filtering Lemma
- 22 Elements of the Proof: 2. A Markov Random Field Property
- 23 Summary: Beyond Mean-Field Limits
- 24 Infinite d-regular trees
- 25 Unimodular Galton-Watson trees
- 26 Marginal Dynamics on Galton Watson Trees
- 27 Interacting Jump Process Dynamics
- 28 Analogous Convergence Results Assumption
- 29 Convergence Results for Jump Processes (contd.)
- 30 Marginal Dynamics for Jump Processes on A-Regular Trees
- 31 Markovian Approximations to the Local Equations
- 32 Detecting Phase Transitions via Markov Approximations
- 33 Markovian Approximations for Transient Behavior
- 34 Acknowledgment for Numerical Simulations
