Related papers: Power variations for fractional type infinitely di…
In this paper we analyze the asymptotic behavior of the Dirichlet fractional Laplacian $(-\Delta_{\mathbb R^{n+k}})^{s}$, with $s\in (0, 1)$, on bounded domains in $\mathbb R^{n+k}$ that become unbounded in the last $k$-directions. A…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
This is the second of two papers which address the problem of measuring the unredshifted power spectrum of fluctuations from a galaxy survey in optimal fashion. A key quantity is the Fisher matrix, which is the inverse of the covariance…
In this article, we obtain some necessary and sufficient conditions for the boundedness of fractional Hausdorff operators $h_{\Phi,\beta}$ on weighted Lebesgue spaces $(0\leq\beta<1)$, which are fractional variants of Bandaliev-Safarova…
In discrete contexts such as the degree distribution for a graph, \emph{scale-free} has traditionally been \emph{defined} to be \emph{power-law}. We propose a reasonable interpretation of \emph{scale-free}, namely, invariance under the…
In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincar\'e invariance. We present the latest development in the field, in particular the notion of…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…
Based on the Riemann- and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed…
The frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency independent…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted…
We express generalized Cauchy-Stieltjes transforms of some particular Beta distributions (of ultraspherical type generating functions for orthogonal polynomials) as a powered Cauchy-Stieltjes transform of some measure. For suitable values…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
We analyze recent results concerning the hypothesis of a privileged direction in the space-time that is made by considering a background of the Lorentz symmetry violation determined by a fixed spacelike vector field and the analysis of…
We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_i\}_{i \in \left\{1,...,n\right\}^d}$, each distributed according to a one-dimensional natural exponential family $\mathcal F =…
A theory of intermittency differentiation is developed for a general class of 1D Infinitely Divisible Multiplicative Chaos measures. The intermittency invariance of the underlying infinitely divisible field is established and utilized to…
Let ${X_n, n \ge 1}$ be a sequence of stationary associated random variables. For such a sequence, we discuss the limiting behavior of U-statistics based on kernels which are of bounded Hardy-Krause variation.
In the context of the nonminimal Standard-Model Extension a special subset of the CPT-even higher-dimensional operators in the photon sector is discussed from a quantum-field theoretical point of view. The modified dispersion laws, photon…
We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…