3 problems

Let $S$ have the centered semicircular distribution with variance parameter $1$, written $S\sim\mathcal{S}(0,1)$. Let $r$ be real. Semicircular power conjectures. The following ass…

Let $\mathbf{t}_q$ denote the t-distribution with parameter $q$. A probability distribution is freely infinitely divisible (FID) if it is infinitely divisible with respect to free…

Let $\bm{\beta}_{p,q}$ and $\bm{\beta}'_{p,q}$ denote the beta and beta prime distributions, respectively, and let $\bm{\gamma}_p$ denote the gamma distribution, with parameters in…