Related papers: Concentration of product spaces
Malcev described the congruences of the monoid $T_n$ of all full transformations on a finite set $X_n=\{1, \dots,n\}$. Since then, congruences have been characterized in various other monoids of (partial) transformations on $X_n$, such as…
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
We study the relationship between different kinds of convergence of finite signed measures and discuss their metrizability. In particular, we study the concept of basic convergence recently introduced by Khartov [arXiv:2204.13667] and…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric…
We describe the canonical correspondence between set of all finite metric spaces and set of special symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those…
This article considers the question of how much of the mass of an element in a Paley-Wiener space can be concentracted on a given set. We seek bounds in terms of relative densities of the given set. We extend a result of Donoho and Logan…
A set of sequences is said to converge simultaneously if there exists an infinite subset $H$ of the index set $\omega$ such that all sequences converge when restricted to $H$. We discuss simultaneous convergence of sequences in the same or…
We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the…
Symmetric products of curves are important spaces for both geometers and topologists, and increasingly useful objects for physicists. We summarize in this note some of their basic homotopy theoretic properties and derive a handful of known…
For a convergent series with positive terms, we prove that the $\ell^\infty$ product space of bounded subspaces of the Gromov-Hausdorff space can be isometrically embedded into the Gromov-Hausdorff space, where each subspace consists of…
The questions of the measure and finding open intervals in certain sets of sums and products of elements of the middle third Cantor set (or a variant of it), have generated considerable interest recently. A broad general framework that…
We prove a tight subspace concentration inequality for the dual curvature measures of a symmetric convex body.
The possibilities of unlike particle correlations for a study of the space-time asymmetries in particle production, including the sequence of particle emission, are demonstrated.
Exhibiting a new type of measure concentration, we prove uniform concentration bounds for measurable Lipschitz functions on product spaces, where Lipschitz is taken with respect to the metric induced by a weighted covering of the index set…
We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results…
We investigate the notion of concentration locus introduced in \cite{CacUrs22}, in the case of Riemann manifolds sequences and its relationship with the volume of tubes. After providing a general formula for the volume of a tube around a…
The magnitude of metric spaces does not appear to possess a simple, convenient continuity property, and previous studies have presented affirmative results under additional constraints or weaker notions, as well as counterexamples. In this…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
The class of spaces such that their product with every Lindel\"of space is Lindel\"of is not well-understood. We prove a number of new results concerning such productively Lindel\"of spaces with some extra property, mainly assuming the…