Related papers: The strong mixing and the operator-selfdecomposabi…
We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…
The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though…
We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is…
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…
Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…
We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…
We construct strongly mixing invariant measures with full support for operators on F-spaces which satisfy the Frequent Hypercyclicity Criterion. For unilateral backward shifts on sequence spaces, a slight modification shows that one can…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
We point out that double distributions need not vanish at their boundary. Boundary terms do not change the ambiguity inherent in defining double distributions; instead, boundary conditions must be satisfied in order to switch between…
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…