We consider particle systems (also known as point processes) on the line and in the plane
and are particularly interested in “hole” events, when there are no particles in a large disk (or …

A random set of points in Euclidean space is called 'rigid'or 'hyperuniform'if the number of
points falling inside any given region has significantly smaller fluctuations than the …

Consider the Gaussian entire function where {ξk} is a sequence of independent standard
complex Gaussians. This random Taylor series is distinguished by the invariance of its zero …

Stochastic point processes with Coulomb interactions arise in various natural examples of
statistical mechanics, random matrices and optimization problems. Often such systems due …

arXiv:2406.19114v2 [math.CV] 1 Jul 2024 Page 1 arXiv:2406.19114v2 [math.CV] 1 Jul 2024
HOLE PROBABILITIES OF RANDOM ZEROS ON COMPACT RIEMANN SURFACES HAO WU …

In this paper we answer the following question of Ofer Zeitouni and Subhro Ghosh [8], which
arises in the study of zeros of random polynomials [4]. Let P be a polynomial. Consider the …

This article revisits the work by Ofer Zeitouni and Steve Zelditch on large deviations for the
empirical measures of random orthogonal polynomials with iid Gaussian complex …

We prove the universality of the large deviations principle for the empirical measures of
zeros of random polynomials whose coefficients are iid random variables possessing a …

Let $ X $ be a compact Riemann surface and $\mathcal L $ be a positive line bundle on it.
We study the conditional zero expectation of all the holomorphic sections of $\mathcal L^ n …

Let $ u $ be the logarithmic potential of a probability measure $\mu $ in the plane that
satisfies\[u (z)= u (\overline {z}),\quad u (z)\le u (| z|),\quad z\in\mathbb {C},\] and $ m …