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In this article, we provide a unified framework for studying the convergence of rescaled characteristic polynomials of random matrices from various classical ensembles as well as functional convergence results for the Riemann zeta function.…
We examine the asymptotics of the spectral counting function of a compact Riemannian manifold by V.G.~Avakumovic \cite{Avakumovic} and L.~H\"ormander \cite{Hormander-eigen} and show that for the scale of orthogonal and unitary groups ${\bf…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
In the present paper, taking a dynamical point on view, we study the growth rate and asymptotic behavior of the sequences of the Reidemeister numbers and the sequences of the Reidemeister and the Nielsen coincidence numbers. We also prove…
This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include…
We study the construction of exponential frames and Riesz sequences for a class of fractal measures on ${\mathbb R}^d$ generated by infinite convolution of discrete measures using the idea of frame towers and Riesz-sequence towers. The…
We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…
The relation between fixed point and orbit count sequences is investigated from the point of view of linear mappings on the space of arithmetic functions. Spectral and asymptotic properties are derived and several quantities are explicitly…
Let $E$ be an arbitrary closed set on the unit circle $\partial \mathbb{D}$, u be a harmonic function on the unit disk $\mathbb{D}$ satisfying $|u(z)|\lesssim (1-|z|)^\gamma \rho^{-q}(z)$ where $\rho(z)= \mathop{\rm dist}(z, E)$, $\gamma$,…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
We study a 2-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S.Kerov, G.Olshanski and A.Vershik, Comptes Rendus…
We systematically compute improved asymptotic rank bounds for tensors. Using numerical implicitization, we implement the geometric framework of Kaski and Micha{\l}ek across all computationally feasible cases. By detecting the absence of…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…
The paper considers asymptotics of summation functions of additive and multiplicative arithmetic functions. We also study asymptotics of summation functions of natural and prime arguments. Several assertions on this subject are proved and…