This semester we studied Concentration Inequalities. Here are some references:
Ramon van Handel's Probability in High Dimension notes,
Roman Vershynin's High-Dimensional Probability book, and
Stephane Boucheron, Gabo Lugosi, and Pascal Massart's Concentration Inequalities: A Nonasymptotic Theory of Independence
The schedule is:
Aug 31: Introduction (Daecheol)
Sep 7 and Sep 21: Poincaré inequality (Aditya)
Sep 28: Concentration inequalities for subgaussian (Daecheol)
Oct 5: Entropy method (Daecheol)
Oct 12: cancelled because of MPC
Oct 19 & Nov 26 Log-Sobolev inequality (Jaya)
Nov 2 Introduction to optimal transport (Daecheol)
Nov 16 Transportation method (Daecheol)
This semester we decided to dedicate to Stein's Method and its applications.
Tentative schedule of speakers is as follows
Feb 2. Greg – Week 1 – Intro, Binomial approximation, CLT, Berry Esseen theorem, Stein’s Lemma
Feb 9 & 16. Qiang – Week 2&3 – Exchangeable pair approach
Feb 23 & Mar 2. Bob – Week 4&5 – Dependency graph approach
Mar 9 – Cancelled because of SSP (link)
Mar 23 & 30. Daecheol - Week 6&7 – Size bias coupling approach
Apr 6 & 13 .Greg – Week 8&9 – General perturbative approach and general couplings
Apr 20 & 27. Peixue – Week 10 & 11 – Quantum version of Stein Lemma
May 4 & 11. Anant – Week 12 & 13 – Stein method in Machine Learning and Computational statistics
This semester we decided to dedicate to Scaling Limits on particular examples.
Tentative schedule of speakers is as follows
Sept 8 & 15. Bob Krueger
Sept 22. Greg
Sept 29. Igor
Oct 6 & 13. Aditya
Oct 27 & Nov 3. Kesav
Nov 10. Qiang
Dec 1. Activity: likely bowling
This semester we decided to dedicate to variety of topics that may or may not be related to each other.
This semester we decided to dedicate to Coupling Method on particular examples.
This semester we decided to dedicate to Large Deviation Theory.
Feb 11 & 25. Qiang Wu "Cramer's Theorem"
Mar 4 & 11. Peixue Wu "Sanov's Theorem and its generalizations"
Mar 14 & 23. Kesav Krishnan "Contraction principle"
Apr 1 & 8. Grigory Terlov "LDP for random dense graphs"
Apr 15 & 22. Robert Kruger "Upper tails for triangles"
This semester we decided to dedicate to Interacting Particle Systems. We are planning to roughly follow the book by Thomas M. Liggett (https://www.springer.com/gp/book/9783540226178) and notes by Jan M. Swart (https://arxiv.org/abs/1703.10007).
Sept 10 & 17. Grigory Terlov "Introduction, phase transitions, and Poisson construction"
Sept 24 & Oct 1. Qiang Wu "The mean-field limit"
Oct 8 & 15. Kesav Krishnan "Ergodicity"
Oct 22 & 29. Peixue Wu "Monotonicity principle"
Nov 5 & 12. Daesung Kim "Duality principle"
This semester we decided to dedicate to Random matrix theory. We are planning to roughly follow the book by Anderson, Guinnet and Zeitouni (http://www.wisdom.weizmann.ac.il/~zeitouni/cupbook.pdf).
Jan 30 & Feb 6. Kesav Krishnan "Stieltjes transform and The Semicircule Law for Wigner Matrices"
Feb 13 & 20. Peixue Wu "Distribution of eigenvalues of random matrices"
Feb 27 & Mar 12. Qiang Wu "Tracy-Widom distribution and spherical spin glass"
Apr 2 & 9. Haojian Li "Universality and Local Universality"
Apr 16 and 23. Ryan Britton "Free Probability"
Sept 5 & 12. Grigory Terlov "Random Planar Maps"
Sept 19 & 26. Kesav Krishnan "The Yang Mills Problem for Probabilists"
Oct 3 & 10. Qiang Wu "Spin Glasses"
Oct 17 & 24. Peixue Wu "Branching processes"
Oct 31 & Nov 7. Yuki Inagaki "Diffusion Processes with singular drifts"
Nov 14 & 21. Jianyu Hu "Probabilistic solutions for fluid systems and stochastic Noether-Kelvin theorem"
Jan 24 & 31. Grigory Terlov "Introduction to Percolation Theory"
Feb 7 &14. Kesav Krishnan "An Introduction to Dyson Brownian Motion and Universality"
Feb 21 & 28. Felix Clemen "Thresholds functions for Random Graphs"
Mar 7 &14. Partha S. Dey "Proof of CLT through entropy"
Mar 28 & Apr 2. Han "Markov Processes"
Apr 11 & 18. Qiang Wu "Local Limit Theorems"
Apr 28. Peixue Wu "Coupling and its applications"