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Abstract

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.