Related papers: Foundations of regular variation on topological sp…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. The unifying theme is the Popa groups of our title viewed as locally…
We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…
The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
In this article, we consider a series $X(t)=\sum_{j \geq 1}\Psi_j(t) Z_j(t),t \in [0,1]$ of random processes with sample paths in the space $D=D[0,1]$ of c\`adl\`ag functions (i.e. right-continuous functions with left limits) on $[0,1]$. We…
TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…
We define a new topological summary for data that we call the persistence landscape. Since this summary lies in a vector space, it is easy to combine with tools from statistics and machine learning, in contrast to the standard topological…
Fundamental constants are a cornerstone of the physical laws. Any constant varying in space and/or time would signal a violation of local position invariance and be associated with a violation of the universality of free fall, and hence of…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Cosmography is a model-independent phenomenological approach to observational cosmology, relying on Taylor series expansions of physical quantities as a function of the cosmological redshift or other analogous variables. A recent work…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…
It has been known for years how random height variations of a repeated nano-scale structure can give rise to smooth angular color variations instead of the well-known diffraction pattern experienced if no randomization is present. However,…
The first formal development of functions with bounded variation in normed spaces is attributed to Chistyakov [5], and was later extended to the context of 2-normed spaces by Cure, Ferrer S., and Ferrer V. [6]. In this paper, we elaborate…
Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process,…