20 citations · 55 across the 15 of their papers we have counts for
8 papers · 1 filter
The image of random analytic functions: coverage of the complex plane via branching processes
Alon Nishry, Elliot Paquette
We consider the range of random analytic functions with finite radius of convergence. We show that any unbounded random Taylor series with rotationally invariant coefficients has d…
Large charge fluctuations in the hierarchical Coulomb gas
Alon Nishry, Oren Yakir
The two-dimensional one-component plasma (OCP) is a model of electrically charged particles which are embedded in a uniform background of the opposite charge, and interact through…
Gaussian complex zeroes are not always normal: limit theorems on the disc
Jeremiah Buckley, Alon Nishry
We study the zeroes of a family of random holomorphic functions on the unit disc, distinguished by their invariance with respect to the hyperbolic geometry. Our main finding is a t…
Universality for outliers in weakly confined Coulomb-type systems
Raphael Butez, David García-Zelada, Alon Nishry +1
This work concerns weakly confined particle systems in the plane, characterized by a large number of outliers away from a droplet where the bulk of the particles accumulate in the…
Fluctuations for Zeros of Gaussian Taylor Series
Avner Kiro, Alon Nishry
We study fluctuations in the number of zeros of random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When the functions are enti…
Rigidity for zero sets of Gaussian entire functions
Avner Kiro, Alon Nishry
In this note we consider a certain class of Gaussian entire functions, characterized by some asymptotic properties of their covariance kernels, which we call admissible (as defined…
Point processes, hole events, and large deviations: random complex zeros and Coulomb gases
Subhro Ghosh, Alon Nishry
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…
Entire functions of exponential type represented by pseudo-random and random Taylor series
Alexander Borichev, Alon Nishry, Mikhail Sodin
We study the influence of the multipliers on the angular distribution of zeroes of the Taylor series \[ F_ξ(z) = \sum_{n\ge 0} ξ(n) \frac{z^n}{n!}\,. \] We show that the dis…