Related papers: Asymptotics of the Airy-kernel determinant
A model to estimate the asymptotic isotropic mutual information of a multiantenna channel is considered. Using a block-based dynamics and the angle diversity of the system, we derived what may be thought of as the operator-valued version of…
We work out a generalization of the Szeg\"o limit theorems on the determinant of large matrices. We focus on matrices with nonzero leading principal minors and elements that decay to zero exponentially fast with the distance from the main…
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
The asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which describes the R\'enyi entropy of order $p$ of the associated quantum oscillator probability density, is determined for $n\to\infty$ and $p>0$. Then, it is applied…
We give an analytic proof of the asymptotic behaviour of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order…
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…
We study the asymptotic behavior of a special smooth solution y(x,t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of Hamiltonian perturbations of hyperbolic equations. The…
We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the…
The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…
In this paper, we provide a review on the kernel method, which is one of the options for characterizing so-called exact tail asymptotic properties in stationary probabilities of two-dimensional random walks, discrete or continuous (or…
A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in…
In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…
We study nonintersecting Brownian motions with two prescribed starting and ending positions, in the neighborhood of a tacnode in the time-space plane. Several expressions have been obtained in the literature for the critical correlation…
Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from…
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…
In this paper, we study the asymptotics of the Hahn polynomials Q_n(x; {\alpha}, {\beta}, N) as the degree n grows to infinity, when the parameters {\alpha} and {\beta} are fixed and the ratio of n/N = c is a constant in the interval (0,…
The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes…