arXiv subjects

Maryna Manskova

Publications and source records attributed to Maryna Manskova.

4 recordsLinked to original sources

arXiv2026

On the pair correlation statistics for determinantal point processes on the sphere

In this paper, we study the expected value of the pair correlation statistics of randomized point configurations on the sphere, with the emphasis on point configurations generated by determinantal point processes. We study the cases of the spherical ensemble, the harmonic ensemble, and jittered sampling, and compare our results with those for the ''truly random'' (i.i.d.) case. Our results give evidence of the small-scale repulsion phenomenon which is characteristic for determinantal point processes, while on larger scales there is good agreement between all our studied cases and the i.i.d. case.

math.PR↗

arXiv2025

Arbitrarily long strings of consecutive primes in special sets

Let $F(x)$ be a function of the form $ \sum_{i=1}^r d_i x^{ρ_i}$ where $d_1,\ldots,d_r\in\mathbb{R}$, $0 \leq ρ_1 < \ldots < ρ_r,$ $ρ_r \not\in \mathbb{Z},ρ_i \in \mathbb{R}$ for $ 1 \leq i \leq r$ and $d_r\not=0$. We prove that sets of the form $\{ n \in \mathbb{N}: \{ F(n) \} \in U \}$ for any non-empty open set $U \subset [0,1)$ contain arbitrarily long strings of consecutive primes.

math.NT↗

arXiv2025

Moment generating functions and moderate deviation principles for lacunary trigonometric sums

In a recent paper, Aistleitner, Gantert, Kabluchko, Prochno and Ramanan studied large deviation principles (LDPs) for lacunary trigonometric sums $\sum_{n=1}^N \cos(2 πn_k x)$, where the sequence $(n_k)_{k \geq 1}$ satisfies the Hadamard gap condition $n_{k+1} / n_k \geq q > 1$ for $k \geq 1$. A crucial ingredient in their work were asymptotic estimates for the moment generating function (MGF) of such sums, which turned out to depend on the fine arithmetic structure of the sequence $(n_k)_{k \geq 1}$ in an intricate way. In the present paper we carry out a detailed study of the MGF for lacunary trigonometric sums (without any structural assumptions on the underlying sequence, other than lacunarity), and we determine the sharp threshold where arithmetic effects start to play a role. As an application, we prove moderate deviation principles for lacunary trigonometric sums, and show that the tail probabilities are in accordance with Gaussian behavior throughout the whole range between the central limit theorem and the LDP regime.

math.PR↗

arXiv2025

Open problems UP24

The conference Unexpected Phenomena in Energy Minimization and Polarization, held in Sofia, Bulgaria in 2024, provided a platform for researchers to discuss and propose challenging open questions across various fields, such as potential theory, approximation, special functions, point configurations, lattices, and numerical analysis. The open problems sessions were productive, fruitful and led to a range of interesting questions. In this document, we present these open problems.

math.CA↗