A random sample size version of the central limit theorem is obtained for a general class of symmetric statistics based on uniform spacings. An important application to goodness of fit test for a Poisson process is discussed.

1 Overview 3 1.1 Dimer definitions . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Uniform random tilings . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Limit shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Facets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5.1 Erg...

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L∞. This allows to get the vanishing viscosity limit to the incompressible Euler system from a s...

We prove existence and uniqueness of solutions to the Klein-Gordon-Zakharov system in the energy space H × L on some time interval which is uniform with respect to two large parameters c and α. These two parameter correspond to the plasma frequency and the sound speed. In the simultaneous high-frequency and subsonic limit, we recover the nonlinear Schrödinger system at the limit. We are also ab...

In this paper the asymptotic analysis of multi-channel queueing networks is developed. Service processes in a heavy traffic regime for [ | , and -models are considered. Functional limit theorems of diffusion approximation type for service processes are formulated under convergence in uniform topology. A limit non-Markov Gaussian process is constructed, its correlation characteristics are repres...

An asymptotic-induced scheme for nonstationary transport equations with the diffusion scaling is developed. The scheme works uniformly for all ranges of mean-free paths. It is based on the asymptotic analysis of the diffusion limit of the transport equation. A theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven. Moreove...

We introduce a one parameter family of non-linear, non-local integrodifferential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of th...

The electro-diffusion model, which arises in electrohydrodynamics, is a coupling between the Nernst-Planck-Poisson system and the incompressible Navier-Stokes equations. For the generally smooth doping profile, the quasineutral limit (zero-Debye-length limit) is justified rigorously in Sobolev norm uniformly in time. The proof is based on the elaborate energy analysis and the key point is to es...

Abstract. We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes to Wiener process in the Skorohod space endowed by the topology of uniform convergence. An integral type almost sure version of this limit theorem i...

Let (Xn)n∈ω be a sequence of uniform spaces such that each space Xn is a closed subspace in Xn+1. We give an explicit description of the topology and uniformity of the direct limit u-lim −→ Xn of the sequence (Xn) in the category of uniform spaces. This description implies that a function f : u-lim −→ Xn → Y to a uniform space Y is continuous if for every n ∈ N the restriction f |Xn is continuo...