Kavita Ramanan - Interacting Stochastic Processes on Sparse Random Graphs

Kavita Ramanan - Interacting Stochastic Processes on Sparse Random Graphs

International Mathematical Union via YouTube Direct link

Intro

1 of 34

1 of 34

Intro

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Kavita Ramanan - Interacting Stochastic Processes on Sparse Random Graphs

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

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