Alexander Volberg - Poincaré Inequalities on Hamming Cube - Analysis, Combinatorics, Probability

Explore the intricacies of Poincaré inequalities on the Hamming cube in this 45-minute lecture by Alexander Volberg at the Hausdorff Center for Mathematics. Delve into the improvement of the constant π/2 in the L^1-Poincaré inequality, comparing it to the known sharp constant in Gaussian space. Examine the work of L. Ben Efraim and F. Lust-Piquard, and discover a new estimate that proves the constant is strictly smaller than π/2. Investigate various proofs and approaches, including boundary edges, geometric estimators, and production spaces. Analyze the relationship between C1 and sqrt(π/2), and explore related topics such as the central limit theorem, random variables, and computer-to-computer interactions. Gain insights into this complex mathematical landscape, bridging analysis, combinatorics, and probability theory.

Introduction
Boundary edges
Markoulis
Geometric estimator
Production space
Promotion
Explanation
Interpretation
Estimating
Correction estimates
Commutative problem
Proof
Theory
Kernels
Random variables
Computer to computer
Central limit theorem
C dual