Stochastic processes for Boolean profit

Abstract: Not even influence inequalities for Boolean functions can escape the long arm of stochastic processes. I will present a (relatively) natural stochastic process which turns Boolean functions and their derivatives into jump-process martingales. There is much to profit from analyzing the individual paths of these processes: Using stopping times and level inequalities, we will prove a conjecture of Talagrand relating edge boundaries and the influences, and show stability of KKL, isoperimetric, and Talagrand's influence inequality. The technique (mostly) bypasses hypercontractivity. Work with Ronen Eldan.

dynamical systemsprobability

Audience: researchers in the topic

( slides | video )

Horowitz seminar on probability, ergodic theory and dynamical systems