All Questions

By "spectrum of a convex body", I mean: start with a convex body $B$ in $\mathbb{R}^d$, then consider the corresponding $d \times d$ covariance matrix resulting from a uniform distribution over $B$ -- ...

Let $P_n$ be a "random convex polyhedron" in $\mathbb{R}^3$ of $n$ vertices, where "random" could follow any one of a number of models: (1) the convex hull of $n$ points randomly and uniformly ...

For a measure $\mu$ supported on a convex body $K$, what are the conditions on $\mu$ and $K$ to satisfy a Log-Sobolev inequality of the form: $$\int f^{2} \log f^{2}\,d\mu -\int f^{2}\,d\mu \log\left(\...

Consider a convex compact set $K\subset R^n$ (with non-empty interior if that helps). Let $\Pi_K:R^n\to K$ be the projection onto $K$, defined as $$ \Pi_K(x) = \operatorname{argmin}_{k\in K} \|k-x\| $$...

I am wondering if any convex geometers/probabilists have looked at the following question: Given $n$ randomly distributed (not sure what assumption to put there) points in $\mathbb{R}^d$, for each ...