## Thursday, March 08, 2007

### Shouts-out

On the topic of hypercontractivity, I just wanted to give a couple of shouts-out. Back when I learned this stuff, I didn't have any intuition at all about the hypercontractivity theorem, and would ask all and sundry, "Do you have any idea what's really going on here?" "Do you have any idea what's really going on here?"

Krzysztof Oleszkiewicz showed me the slick, simple induction proof of $(2, 4, 1/\sqrt{3}^d)$-hypercontractivity for boolean functions with degree at most $d$. I asked him, "Who is this proof due to? You?" He said, "No no no, not me. Folklore, I guess."

Top Analysis-of-Boolean-Functions expert Guy Kindler showed me the nice level-sets, geometrical-picture proof of the Two-Point Inequality.

So -- thanks to both of them!