On the isotropic constant of marginals

Grigoris Paouris¹

¹ Department of Mathematics Texas A & M University College Station, TX 77843, U.S.A.

Studia Mathematica, Tome 212 (2012) no. 3, pp. 219-236

Résumé

We show that if $\mu_{1}, \ldots , \mu_{m}$ are $\log$-concave subgaussian or supergaussian probability measures in $\mathbb R^{n_{i}}$, $i\le m$, then for every $F$ in the Grassmannian $G_{N,n}$, where $N=n_{1}+\cdots +n_{m}$ and $n N$, the isotropic constant of the marginal of the product of these measures, $\pi_{F} (\mu_{1}\otimes \cdots \otimes \mu_{m})$, is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.

Détail

DOI : 10.4064/sm212-3-2

Keywords: ldots log concave subgaussian supergaussian probability measures mathbb every grassmannian where cdots isotropic constant marginal product these measures otimes cdots otimes bounded extends known results bounds isotropic constant larger class measures