Abstract: We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and inâ€¦ (More)

We study the empirical measure LAn of the eigenvalues of nonnormal square matrices of the form An = UnTnVn with Un, Vn independent Haar distributed on the unitary group and Tn real diagonal. We showâ€¦ (More)

Given an nÃ— n complex matrix A, let Î¼A(x, y) := 1 n |{1 â‰¤ i â‰¤ n,ReÎ»i â‰¤ x, ImÎ»i â‰¤ y}| be the empirical spectral distribution (ESD) of its eigenvalues Î»i âˆˆ C, i = 1, . . . n. We consider the limitingâ€¦ (More)

Abstract We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Zâ€¦ (More)

We consider the point process of zeroes of certain Gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radiusâ€¦ (More)

1 Leading up to the results Singular points of random matrix-valued analytic functions are a common generalization of eigenvalues of random matrices and zeros of random polynomials. The setting isâ€¦ (More)

Zeros of Random Analytic Functions The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for manyâ€¦ (More)

We introduce a new method for studying universality of random matrices. Let Tn be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show thatâ€¦ (More)

A result of Zyczkowski and Sommers [J. Phys. A 33, 2045â€“2057 (2000)] gives the eigenvalue probability density function for the top N Ã—N sub-block of a Haar distributed matrix from U(N + n). In theâ€¦ (More)