Related papers: Asymptotics of polynomials and eigenfunctions

In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…

We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more.…

We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic…

We study the asymptotic distribution of roots of Lommel polynomials as polynomials of the order with a variable and purely imaginary argument. The roots are complex and accumulate on certain curves in the complex plane. We prove existence…

For the generalized Jacobi, Laguerre and Hermite polynomials $P_n^{(\alpha_n, \beta_n)} (x), L_n^{(\alpha_n)} (x),$\break $H_n^{(\gamma_n)} (x)$ the limit distributions of the zeros are found, when the sequences $\alpha_n$ or $\beta_n$ tend…

For small range of $p>2$, we improve the $L^p$ bounds of eigenfunctions of the Laplacian on negatively curved manifolds. Our improvement is by a power of logarithm for a full density sequence of eigenfunctions. We also derive improvements…

Let f be a dominating meromorphic self-map of a compact Kahler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of f using the metric entropy and the dynamical degrees of f. We deduce the hyperbolicity of…

The primary purpose of this article is to study the asymptotic and numerical estimates in detail for higher degree polynomials in $\pi(x)$ having a general expression of the form, \begin{align*} P(\pi(x)) - \frac{e x}{\log x} Q(\pi(x/e)) +…

In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of…

We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients $\alpha_{n,N}$ when the ratio $n/N$ converges as $n,N\to\infty$. First, we give a streamlined proof of ratio asymptotics for…

In the recent work arXiv:1311.3999, the authors proved that real analytic manifolds $(M, g)$ with maximal eigenfunction growth must have a self-focal point p whose first return map has an invariant L1 measure on $S^*_p M$. In this addendum…

Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued…

A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition. An alternative partition is revealed by considering a set of…

This paper is concerned with the asymptotic behavior of the generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media where one scale is fixed and another one…

We study the dynamics of a bimeromorphic selfmap of a compact complex K\"ahler surface $X$. Under a natural geometric hypothesis, we construct an invariant probability measure, which is mixing, hyperbolic and of maximal entropy. The proof…

The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…

We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by…

We compute the pointwise asymptotics of orthogonal polynomials with respect to a general class of pure point measures supported on finite sets as both the number of nodes of the measure and also the degree of the orthogonal polynomials…

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the…