Once on the forefront of mathematical research in America, the asymptotics of the solutions of linear recurrence equations is now almost forgotten, especially by the people who need it most, namely combinatorists and computer scientists. Here we present this theory in a concise form and give a number of examples that should enable the practicing combinatorist and computer scientist to include t...

This is the first in a series of two papers aiming to establish sharp spectral asymptotics for Steklov type problems on planar domains with corners. In the present paper we focus on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We pr...

We study the ultraviolet asymptotics in non-simply laced affine Toda theories considering them as perturbed non-affine Toda theories, which possess the extended conformal symmetry. We calculate the reflection amplitudes, in non-affine Toda theories and use them to derive the quantization condition for the vacuum wave function, describing zero-mode dynamics. The solution of this quantization con...

ABSTRACT. The plane waveguides with corners considered here are infinite V-shaped strips with constant thickness. They are parametrized by their sole opening angle. We study the eigenpairs of the Dirichlet Laplacian in such domains when this angle tends to 0. We provide multi-scale asymptotics for eigenpairs associated with the lowest eigenvalues. For this, we investigate the eigenpairs of a on...

Let (Xt)t≥0 be a R-valued stationary reversible diffusion process. We investigate the asymptotic behavior of MT := max0≤t≤T |Xt|, where | · | is the Euclidean norm in R. The aim of this paper is to characterize the tail asymptotics of MT for fixed T > 0 as well as the long time behavior of MT as T → ∞. This is related to spectral asymptotics of the generator of (Xt)t≥0 subject to Dirichlet boun...

We discuss asymptotics of the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold. We obtain an asymptotic formula for the average of the number of states. Furthermore, when the operator has integer eigenvalues and the periodic orbits of period less than 2π of the classical mechanics form clean submanifo...

Abstract. We consider lattice walks in R confined to the region 0 < x1 < x2... < xk with fixed (but arbitrary) starting and end points. The walks are required to be ”reflectable”, that is, we assume that the number of paths can be counted using the reflection principle. The main result is an asymptotic formula for the total number of walks of length n for a general class of walks as n tends to ...

The high order corrections to renormalon are considered. Each new type of insertions into the renormalon chain of graphs generates the correction to the asymptotics of perturbation theory of the order of ∼ 1. However, this series of corrections to the asymptotics is not the asymptotic one (i.e. the m-th correction does not grow like m!). The summation of these corrections for UV renormalon may ...

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above w...