3 problems

Let $X$ be a heavy-tailed stable random matrix with unitary invariance, meaning that its eigenvalues and eigenvectors are uncorrelated. Suppose that the largest eigenvalues are con…

For $\alpha\in[0,1]$, say that $\alpha$ is of type $\omega$ if there are only finitely many pairs $(a,q)$ satisfying $\lvert\alpha-a/q\rvert<q^{-\omega}$. Let $a/q$ range over the…

Let $Y$ be uniformly distributed on $[0,1)$, and for $N\in\mathbb{N}$ and $0<L\leq N$ define the random variable … Here $\operatorname{Po}(L)$ denotes a Poisson-distributed random…