Abstract: Let X be a generalised symmetrised Dirichlet random vector inIR, k ≥ 2, and let tn ∈IRk, n ≥ 1 be such that limn→∞ P {X > tn} = 0. In this paper we derive an exact asymptotic expansion of P {X > tn} as n → ∞, assuming that the associated random radius of X has distribution function in the Gumbel max-domain of attraction.

A class of infinite-dimensional discrete-time state operators is exhibited as concrete instances of power-bounded operators that are not similar to contractions. It is shown that such discrete-time systems arise from sampled feedback control of unstable continuoustime systems. The asymptotic behavior of the state operators of these discrete systems is not intimately related to their spectral ra...

We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and Féral for perturbed Wigner matrices as w...

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for ...

Asymptotic formula are derived for the number of n x m matrices of fixed rank k with rational integral coefficients that are contained in a Euclidean ball of radius T in R" *m . It is assumed that n > m > k > 1 are fixed, and the asymptotics are valid as T tends to infinity. The methods used are elementary.

In this paper, we consider some properties of hyperbolic polyhedra, both common with Euclidean and specific. Asymptotic behavior metric characteristics polyhedra in the n-dimensional space is examined cases where parameters change dimension unboundedly increases; particular, radius inscribed sphere a polyhedron estimated its asymptotic obtained. connection this, problem estimating minimal numbe...

To model biochemical systems in which both noise in the chemical reaction process and spatial movement of molecules is important, both the reaction-diffusion master equation (RDME) and Smoluchowski diffusion-limited reaction (SDLR) partial differential equation (PDE) models have been used. In previous work we showed that the solution to the RDME may be interpreted as an asymptotic approximation...

We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering problem. Uniform asymptotic expansions needed are obtained from the Lippmann-Schwinger equation. The general results derived are applied to the background of a fin...

By applying the three-dimensional total internal reflection velocimetry (3D-TIRV) technique to freely suspended micron-sized fluorescent particles, we are able to simultaneously observe the three-dimensional anisotropic hindered diffusion for values of the gap-size-to-radius ratio much less than one. We demonstrate that the 3D-TIRV can be used to accurately track freely suspended 1.5-mum radius...

A model for the condensation of a dusty plasma is constructed by considering the spherical shielding layers surrounding a dust grain test particle. The collisionless region less than a collision mean free path from the test particle is shown to separate into three concentric layers, each having distinct physics. The method of matched asymptotic expansions is invoked at the interfaces between th...