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 reprove an inequality of Talagrand relating edge boundaries and the influences, and say something about functions which almost saturate the inequality. The technique (mostly) bypasses hypercontractivity. Work with Ronen Eldan.

Computer scienceMathematicsPhysics

Audience: researchers in the topic

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