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The $\alpha$-stable distributions introduced by L\'evy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study…
We present a study of the polarization of the $\Upsilon(1S)$ and $\Upsilon(2S)$ states using a $1.3 $ fb$^{-1}$ data sample collected by the D0 experiment in 2002--2006 during Run II of the Fermilab Tevatron Collider. We measure the…
We study the one-dimensional Levy stable density distributions g(alpha, beta; x) for -infty < x < infty, for rational values of index alpha and the asymmetry parameter beta: alpha = l/k and beta = (l - 2r)/k, where l, k and r are positive…
A wavelet space-scale decomposition (SSD) analysis of large scale structures in the universe has been developed. The SSD method of identifying and measuring structures in the spatial distribution of objects has been demonstrated. The…
The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these…
We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $\alpha$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider…
Elastic and structural properties of $\beta$-Ga$_2$O$_3$ and $\alpha$-Ga$_2$O$_3$ are investigated from first principles. The full elastic tensors and elastic moduli of both phases at $0$ K are computed in the framework of semi-local…
We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal {O}(\alpha_s)$. Unlike the existing calculations in the literature,…
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible…
We introduce a new approach to modeling transition distribution amplitudes (TDAs) for the processes $e p \to e n \pi^+$ and $e p \to e p \pi^0$. The modeling is flexible, constrained by sparsely available experimental data, and satisfies…
To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In the work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak…
As for the Fourier transforms of positive and integrable functions supported in the unit interval, we make a list of improvements for P\'olya's results on the distribution of their positive zeros and give new sufficient conditions under…
Multistable distributions, which have been introduced recently by Falconer, L\'evy V\'ehel and their co-authors, are natural generalizations of symmetric "alpha" stable distributions; roughly speaking, they are obtained by replacing the…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
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…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…