Related papers: Concentration of product spaces

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

We study the semistability of the tensor product of hermitian vector bundles by using the $\varepsilon$-tensor product and the geometric (semi)stability of vector subspaces in the tensor product of two vector spaces.

This paper introduces product relation correlation, a measure of product relatedness that assesses the extent to which products may function as substitutes or complements through analysis of shared purchasing patterns. Product relation…

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…

In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…

We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…

For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.

We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.

The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay…

This survey is dedicated to a new direction in the theory of dynamical systems: the dynamics of metrics in measure spaces and new (catalytic) invariants of transformations with invariant measure. A space equipped with a measure and a metric…

We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of…

We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces…

Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.

We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…

In this paper, from the viewpoint of the concentration theory of maps, we study a compact group and a L\'{e}vy group action to a large class of metric spaces, such as R-trees, doubling spaces, metric graphs, and Hadamard manifolds.

The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…

We study locally compact convergence groups, in particular the link between the convergence property and the Specker compactifications (a genaralization of the ends) of a group.

A metric measure space is a complete separable metric space equipped with probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on…

We use the trimming transformations to study the tight span of a metric space.