New examples for the KLS conjecture

Nolwen Huet (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We show that the conjecture of Kannan, Lov\'{a}sz and Simonovits is true for log-concave measures of the form $\rho(|x|_B)dx$ on $\R^n$ and $\rho(t,|x|_B) dx$ on $\R^{1+n}$, 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.

Mots clés: KLS conjecture

Mots clés: log-concave measures; Poincaré inequality; KLS conjecture.

Domaines: Probabilités [math.PR]

Nolwen Huet. New examples for the KLS conjecture. 2010. ⟨hal-00466762v2⟩