Related papers: On the Geroch-Traschen class of metrics

We study the non-asymptotic behavior of Coulomb gases in dimension two and more. Such gases are modeled by an exchangeable Boltzmann-Gibbs measure with a singular two-body interaction. We obtain concentration of measure inequalities for the…

We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, non-degenerated and stationary Gaussian field $(f(x), {x \in \mathbb R^d})$. Under mild conditions, we…

For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…

We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same…

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of {\em Colombeau type} in the sense that it contains a copy of the space of Schwartz…

In this work, we consider sequence of metrics with almost non-negative scalar curvature on torus. We show that if the sequence is uniformly conformal to another sequence of metrics with uniformly controlled geometry, then it converges to a…

We say that a distribution is harmonic if it is harmonic when considered as a section of a Grassmann bundle. We find new examples of harmonic distributions and show nonexistense of harmonic distrubutions on some Riemannian manifolds by two…

This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…

The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…

The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…

We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the…

We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…

Let $H < G$ both be noncompact connected semisimple real algebraic groups where the former is maximal proper and $\Gamma < G$ be a lattice. Building on the work of Gorodnik-Weiss, we refine their techniques and obtain effective results.…

For Riem(M) the space of Riemannian metrics over a compact 3-manifold without boundary $M$, we study topological properties of the dense open subspace Riem'(M) of metrics which possess no Killing vectors. Given the stratification of…

This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…

We present necessary and sufficient conditions on systems of random variables for them to possess a lacunary subsystem equivalent in distribution to the Rademacher system on the segment [0,1]. In particular, every uniformly bounded…

We extend the definition of the Lerch distribution to the set of nonnegative integers for greater applicability to modeling count data. We express its properties in terms of Lerch's transcendent, and study its unimodality, hazard function…