" The book examines in some depth two important classes of point processes, determinantal
processes and" Gaussian zeros", ie, zeros of random analytic functions with Gaussian …

These expository notes are centered around the circular law theorem, which states that the
empirical spectral distribution of an× n random matrix with iid entries of variance 1/n tends to …

Go fu (Z): E an zn,(1) n= 0 a where {n} n= 0 are independent standard complex Gaussian
random variables (with density eZ~/Tr). The radius of convergence of the series is as 1, and …

In this paper, we establish some local universality results concerning the correlation
functions of the zeroes of random polynomials with independent coefficients. More precisely …

Abstract Let 0,1,... be independent identically distributed complex-valued random variables
such that E\log(1+|0|)<∞. We consider random analytic functions of the form …

Let $ L $ be a holomorphic line bundle over a compact complex projective Hermitian
manifold $ X. $ Any fixed smooth hermitian metric $\phi $ on $ L $ induces a Hilbert space …

An efficient and robust algorithm and a Matlab code ratdisk are presented for rational
interpolation or linearized least-squares approximation of a function based on its values at …

Let $(L, he^{-u}) $ be a pseudoeffective line bundle on an $ n $-dimensional compact K\"
ahler manifold $ X $. Let $ h^ 0 (X, L^ k\otimes\mathcal I (ku)) $ be the dimension of the …

For a regular compact set $ K $ in $ C^ m $ and a measure $\mu $ on $ K $ satisfying the
Bernstein-Markov inequality, we consider the ensemble $ P_N $ of polynomials of degree …

There is a natural pluripotential-theoretic extremal function VK, Q associated to a closed
subset K of ℂ m C^m and a real-valued, continuous function Q on K. We define random …