Reversing Hypercontractivity

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Shows a uniform reverse hypercontractivity inequality: for any product space and any nonnegative f, T_t raises q‑seminorms above p‑seminorms with no factor log(1/alpha). Proof uses one‑dimensional reduction, tensorization, reverse Hölder and a monotone family of p‑log‑Sobolev inequalities (parametrized so constants scale like p^2/(4(p−1))). Consequences include explicit lower bounds for P[x∈A,y∈B] for rho‑correlated cubes, links to modified log‑Sobolev and expander‑mixing, and a counterexample to naive plurality stability for three‑part partitions at small rho.

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1. 0:00Start
2. 6:23Hyper-contractive estimates for discrete spaces
3. 7:12Reverse-Hyper-Contractive inequalities: What?
4. 11:57Why is it true? Borell's argument
5. 14:13Borell's argument continued
6. 21:36Social Choice Applications
7. 22:08Hyper and Reverse-Hyper Contractive inequalities
8. 23:17Our Results (M-Oleszkiewicz-Sen-11)
9. 31:27Markov Chain Applications (M-Oleszkiewicz-Sen-11)
10. 31:57A Queueing Theory Application (M-Oleszkiewicz-Sen-11)
11. 34:14Definition of logSob
12. 35:14LogSob - Easy facts
13. 35:46Comparison of Dirichlet forms
14. 36:42Borell's Stability Result
15. 37:28Gaussian Isoperimetry for 3-partitions
16. 41:14The case of the missing candidate
17. 44:21The case of biased elections