2 problems

Let $G$ be distributed according to the truncated unitary ensemble $\mathrm{TUE}(N,M)$, let $\mathscr{O}_{ii}$ denote its diagonal overlap, and let $\lambda_1,\dots,\lambda_N$ be t…

Let $p=p_n$ satisfy $p_n\to\infty$, and let $\mathbf{z}_1,\ldots,\mathbf{z}_{p_n}$ be the eigenvalues of the truncated circular unitary matrix. Assume that the truncation parameter…