Related papers: Noncommutative Lebesgue decomposition with applica…
We construct asymptotic expansions of Laplace type for the time-dependent quantum averages for Bose systems with many degrees of freedom, initially populated in coherent states. These solutions are localized in phase space, and they are…
Taking up a variational viewpoint, we present some nonlocal-to-local asymptotic results for various kinds of integral functionals. The content of the thesis comprises the contributions first appeared in some research papers in collaboration…
In this article we survey the development of generic and coarse computability and the main results on how classical asymptotic density interacts with the theory of computability.
We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of…
The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven…
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in…
Given two parties performing experiments in separate laboratories, we provide a diagrammatic formulation of what it means for the joint statistics of their experiments to satisfy local realism. In particular, we show that the principles of…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more…
In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions of physical space which are under the influence of some local, time-dependent…
Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…
We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of inner Galois extensions $L/K$ of fixed degree and center…
We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…
In this paper, we study twist deformed quantum field theories obtained by combining the Wightman axiomatic approach with the idea of spacetime noncommutativity. We prove that the deformed fields with deformation parameters of opposite sign…
We formulate an equivalence relation between nonlocal quantum fields, generalizing the relative locality which was studied by Borchers in the framework of local QFT. The Borchers classes are shown to allow a natural extension involving…
We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized…
We introduce the notion of perturbations of quantum stochastic models using the series product, and establish the asymptotic convergence of sequences of quantum stochastic models under the assumption that they are related via a right series…