February Fourier Talks 2019

Alexander Volberg

Michigan State University

Title:

Improving constant in L1 Poincare inequality on Hamming cube

Abstract:

L1 Poincare inequality on Hamming cube was used by Talagrand to give a quantitative version of Margulis network connectivity theorem. The functional version of this inequality was proved by Ben Efraim and Lust-Piquard in 2007. Their constant was \pi/2.

But in Gaussian case the sharp constant is known by the work of Maurey--Pisier, and it is the square root of that number. So what is the sharp constant on hamming cube? We will show that indeed it is strictly less than pi/2.


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