Related papers: Extreme-value statistics of dimensions determining…
This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole. The presence of the latter influences the extremal index…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
It's the year 2020, and every space and place on- and off-line has been augmented with digital things that observe, record, transmit, and compute, for the purposes of recording endless data traces of what is happening in the world.…
We consider the empirical versions of geometric quantile and halfspace depth, and study their extremal behaviour as a function of the sample size. The objective of this study is to establish connection between the rates of convergence and…
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal…
Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur…
Extremal black holes are studied in a two dimensional model motivated by a dimensional reduction from four dimensions. Their quantum corrected geometry is calculated semiclassically and a mild singularity is shown to appear at the horizon.…
As a useful and elegant tool of extreme value theory, the study of point processes on a metric space is important and necessary for the analyses of heavy-tailed functional data. This paper focuses on the definition and properties of such…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the…
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a…
Exceptional points are singularities of eigenvalues and eigenvectors for complex values of, say, an interaction parameter. They occur universally and are square root branch point singularities of the eigenvalues in the vicinity of level…