Spectral gap for some invariant log-concave probability measures

Details Spectral gap for some invariant log-concave probability measures Spectral gap for some invariant log-concave probability measures

2010-03-25

arxiv.org/abs/1003.4839v3

Mathematics

Probability

To appear in Mathematika. This version can differ from the one published in Mathematika

Scientific paper

We show that the conjecture of Kannan, Lov\'{a}sz, and Simonovits on isoperimetric properties of convex bodies and log-concave measures, is true for log-concave measures of the form $\rho(|x|_B)dx$ on $\mathbb{R}^n$ and $\rho(t,|x|_B) dx$ on $\mathbb{R}^{1+n}$, where $|x|_B$ is the norm associated to any convex body $B$ already satisfying the conjecture. In particular, the conjecture holds for convex bodies of revolution.

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