Approximately gaussian marginals and the hyperplane conjecture

Ronen Eldan; Bo'az Klartag

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arXiv · 1001.0875

Approximately gaussian marginals and the hyperplane conjecture

Ronen Eldan·Bo'az Klartag

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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".

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Ronen Eldan, Bo'az Klartag. 2010-01-06. Approximately gaussian marginals and the hyperplane conjecture. https://arxiv.org/abs/1001.0875

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