On the isotropic constant of marginals

Volume 212 / 2012

Grigoris Paouris Studia Mathematica 212 (2012), 219-236 MSC: Primary 52A40; Secondary 52A38. DOI: 10.4064/sm212-3-2


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.


  • Grigoris PaourisDepartment of Mathematics
    Texas A & M University
    College Station, TX 77843, U.S.A.

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