B. Khoruzhenko

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math.PR2025

On the distribution patterns of zeros for random polynomials with regularly varying coefficients

Zakhar Kabluchko, Boris Khoruzhenko, Alexander Marynych

This paper investigates asymptotic distribution of complex zeros of random polynomials $P_{n} (z) := \sum_{k = 0}^{n} b (k) I^¾_{k} z^{k}$ , as $n \to \infty$ , where $b$ is a regularly varying funct…

math.PR2024

Zeros of conditional Gaussian analytic functions, random sub-unitary matrices and q-series

Yan V. Fyodorov, Boris A. Khoruzhenko, Thomas Prellberg

We investigate radial statistics of zeros of hyperbolic Gaussian Analytic Functions (GAF) of the form $I ¨ (z) = \sum_{k \geq 0} c_{k} z^{k}$ given that $∣ I ¨ (0) ∣^{2} = t$ and assuming coeffici…