On the Suprema of Bernoulli Processes

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Proves the Bernoulli Conjecture: the expected supremum of a Bernoulli process is equivalent (up to universal constants) to the infimum over decompositions of T into two sets so that one part has bounded L1 norm and the other part is controlled by the Gaussian gamma2 functional; only those two mechanisms explain boundedness. Proof uses concentration, a Sudakov-type minoration for signs, and the new use of chopping maps and erasing variables. Applications include random Fourier series bounds and VC-class maximal inequalities.

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1. 0:00Introduction to suprema
2. 3:33Gaussian processes
3. 6:44Majorizing measures
4. 11:59Bernoulli processes
5. 19:06The Bernoulli conjecture
6. 22:10Reverse bounds and tools
7. 25:48Proof techniques
8. 30:59Admissible partitions
9. 34:55Chopping and erasing
10. 38:04Practical applications
11. 44:17VC classes and limits
12. 47:20Empirical processes