Approximately gaussian marginals and the hyperplane conjecture

2010/01/06 by Ronen Eldan, Bo'az Klartag, Eldan, Ronen +2 · 4 citations
Mathematics · #Analytic and geometric function theory #Numerical methods in inverse problems #Point processes and geometric inequalities #math.MG

paper · pdf · doi:10.48550/arxiv.1001.0875

arxiv created 2010/01/06 · arxiv updated 2010/01/14

Abstract

We discuss connections between certain well-known open problems related to the uniform measure on a high-dimensional convex body. In particular, we show that the "thin shell conjecture" implies the "hyperplane conjecture". This extends a result by K. Ball, according to which the stronger "spectral gap conjecture" implies the "hyperplane conjecture".

Cited by

• The KLS constant is O(log^1/4 n)
• Digesting the proof of the sharp thin-shell inequality
• Diffusion Approximations to Schrödinger Bridges on Manifolds
• Thin-shell bounds via parallel coupling

Related

• Thin shell implies spectral gap up to polylog via a stochastic localization scheme
• Further unifying two approaches to the hyperplane conjecture
• On Gaussian Marginals of Uniformly Convex Bodies
• Comments on the floating body and the hyperplane conjecture
• On the hyperplane conjecture for random convex sets