Related papers: Asymptotics for some $q$-hypergeometric polynomial…

Our goal is to find asymptotic formulas for orthonormal polynomials $P_{n}(z)$ with the recurrence coefficients slowly stabilizing as $n\to\infty$. To that end, we develop spectral theory of Jacobi operators with long-range coefficients and…

In this paper, the asymptotic formulas for Eulerian numbers, refined Eulerian numbers and the coefficients of descent polynomials are obtained directly from the spline interpretations of these numbers. Having related these numbers directly…

In this paper we give the asymptotic behavior of type I multiple orthogonal polynomials for a Nikishin system of order two with two disjoint intervals. We use the Riemann-Hilbert problem for multiple orthogonal polynomials and the steepest…

Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in…

We investigate the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled second-order correlation function…

We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by…

We examine the asymptotics of a sequence of lacunary binomial-type polynomials $\wp_n(z)$ as $n\rightarrow\infty$ that have arisen in the problem of the expected number of independent sets of vertices of finite simple graphs. We extend the…

Let G be a bounded region with simply connected closure and having analytic boundary and let mu be a positive measure carried by the closure of G together with finitely many pure points outside G. We provide estimates on the norms of the…

We study asymptotic behavior of the bottom point of the spectrum of convolution type operators in environments with locally periodic microstructure. We show that its limit is described by an additive eigenvalue problem for Hamilton-Jacobi…

In this note, we study the asymptotics of a spherical integral that is a multiplicative counterpart to the well-known Harish-Chandra Itzykson Zuber integral. This counterpart can also be expressed in terms the Heckman-Opdam hypergeometric…

For a class of orthogonal polynomials related to the $q$-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal…

We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained…

In this short note, we consider the question of determining the asymptotics of the volume function near the boundary of the pseudoeffective cone on compact K\"ahler manifolds. We solve the question in a number of cases -- in particular, we…

In this paper we investigate algebraic, differential and asymptotic properties of polynomials $p_n(x)$ that are orthogonal with respect to the complex oscillatory weight $w(x)=e^{i\omega x}$ on the interval $[-1,1]$, where $\omega>0$. We…

We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute…

Our aim in this report is to investigate the asymptotic behavior of Mittag-Leffler functions. We give some estimates involving the Mittag-Leffler functions and their derivatives.

We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such…

There is a vast theory of Chebyshev and residual polynomials and their asymptotic behavior. The former ones maximize the leading coefficient and the latter ones maximize the point evaluation with respect to an $L^\infty$ norm. We study…

We prove limit theorems for the greatest common divisor and the least common multiple of random integers. While the case of integers uniformly distributed on a hypercube with growing size is classical, we look at the uniform distribution on…

We study the uniform asymptotics for the orthogonal polynomials with respect to weights composed of both absolutely continuous measure and discrete measure, by taking a special class of the sieved Pollazek Polynomials as an example. The…