The last video lecture for my CMU course on Analysis of Boolean Functions has just been posted. Except for responding to comments, the blog will be going on hiatus for a little while. Next semester I’ll post the final chapters of the book; there will be between 4 and 7 of them, depending on how much energy I have.
Happy holidays……..
Is a pdf of any sections of the book available?
I’d prefer to wait until the whole thing’s finished, but maybe if there’s enough demand.
Good luck ! We are all looking forward to the final chapters. Would you please list what topics you are planning to cover?
Chapter 8: Generalized domains (Fourier bases, orthogonal decomposition, p-biased analysis, randomized decision tree complexity)
Chapter 9: was going to be additive combinatorics, but as mentioned, I’ll probably skip it
Chapter 10: hypercontractivity and applications (most of this was done in the online CMU videos)
Chapter 11: advanced hypercontractivity (log-Sobolev inequality, Gaussian space/geometry)
Chapter 12: low influences imply high spectra (theorems of Kindler-Safra, DFKO, Benjamini-Kalai-Schramm, Friedgut-Bourgain sharp threshold theorem); I’ll probably skip this chapter, unfortunately
Chapter 13: Invariance Principle (+ majority is stablest)
Chapter 14: Advanced Inapproximability (up to but only partially including the “Raghavendra Theory”) — this one I may or may not get to.