Zakhar Kabluchko

activity

20242026

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13 papers · 1 filter

math.NT2025

Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits

Christoph Aistleitner, Zakhar Kabluchko, Joscha Prochno

We study the asymptotic behavior of cumulants of lacunary trigonometric sums $S_{n} (ω) := \sum_{k = 1}^{n} cos (2 π a_{k} ω)$ , $ω \in [0, 1]$ , and show that cumulant growth is highly sensitiv…

math.PR2025

Zeros of polynomial powers under the heat flow

Antonia Höfert, Jonas Jalowy, Zakhar Kabluchko

We study the zero evolution of high powers of polynomials under the heat flow. For any fixed polynomial $P (z)$ , we prove that the empirical zero distribution of its heat-evolved $n…

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 $P_{n} (z) := \sum_{k = 0}^{n} b (k) ξ_{k} z^{k}$ , as $n \to \infty$ , where $b$ is a regularly varying functi…

math.PR2025

Zero distribution of multiplicative Hermite and Laguerre polynomials

Zakhar Kabluchko

It is well-known that, as $n \to \infty$ , the zero distribution of the $n$ -th Hermite polynomial converges to the semicircular law (the free normal distribution), while the zero dist…

math.CA2025

Zeros and exponential profiles of polynomials II: Examples

Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych

In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real…

math.MG2025

Volumes of Regular Hyperbolic Simplices

Zakhar Kabluchko, Philipp Schange

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.