Approximately gaussian marginals and the hyperplane conjecture

Details Approximately gaussian marginals and the hyperplane conjecture Approximately gaussian marginals and the hyperplane conjecture

2010-01-06

arxiv.org/abs/1001.0875v1

Mathematics

Metric Geometry

Scientific paper

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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