Consider a square random matrix with independent and identically distributed entries of
mean zero and unit variance. We show that as the dimension tends to infinity, the spectral …

We consider a square random matrix of size N of the form A+ Y where A is deterministic and
Y has iid entries with variance 1/N. Under mild assumptions, as N grows the empirical …

We introduce Ginibre-type point processes as determinantal point processes associated
with the eigenspaces corresponding to the so-called Landau levels. The Ginibre point …

We consider the Elliptic Ginibre Ensemble, a family of random matrix models that interpolate
between the Ginibre Ensemble and the Gaussian Unitary Ensemble and such that its …

We establish basic properties of the heat flow on entire holomorphic functions that have
order at most 2. We then look specifically at the action of the heat flow on the Gaussian …

Abstract Consider an N * NN× N Toeplitz matrix T_N TN with symbol a (λ):= ∑ _ ℓ=-d_2^
d_1 a_ ℓ λ^ ℓ a (λ):=∑ ℓ=-d 2 d 1 a ℓ λ ℓ, perturbed by an additive noise matrix N^-γ E_N N-γ …

We study the zeros of random power series with stationary complex Gaussian coefficients,
whose spectral measure is absolutely continuous. We analyze the precise asymptotic …

Consider a random trigonometric polynomial X_n:R→R of the form X_n(t)=∑_k=1^n\left(ξ_k\
sin(kt)+η_k\cos(kt)\right), where (ξ_1,η_1),(ξ_2,η_2),... are independent identically …

We present the continuous wavelet transform (WT) of white Gaussian noise and establish a
connection to the theory of Gaussian analytic functions. Based on this connection, we …

Consider a random polynomial Q_n of degree n+1 whose zeroes are iid random variables
ξ_0,ξ_1,...,ξ_n in the complex plane. We study the pairing between the zeroes of Q_n and its …