6 problems

Circle law for the Dirichlet Markov Ensemble. Almost surely, the empirical spectral distribution converges weakly to $\mathcal{C}_1$:

Let $A_n=(a_{ij})$ and $B_n=(b_{ij})$ be independent real $n\times n$ matrices with i.i.d. entries satisfying … and assume a standard moment condition strong enough to imply the ci…

Circular-law universality conjecture. For constant linear margins and every base measure $\mu$ satisfying the hypothesis of Corollary, the empirical eigenvalue distribution of

Fix $\alpha \in [0,1)$. Let $A=PLQ$ be an $n\times n$ random matrix, where $P$ and $Q$ are independent uniformly chosen permutation matrices and $L$ is independent of $P$ and $Q$.…

Bordenave–Caputo–Chafaï–Tikhomirov conjecture. The convergence in probability

Let $M_n$ be the $n \times n$ random matrix whose entries are iid complex random variables with mean 0 and variance 1. The empirical spectral distribution (ESD) of…