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Let $Z$ be the typical cell of a stationary Poisson hyperplane tessellation in $\mathbb{R}^d$. The distribution of the number of facets $f(Z)$ of the typical cell is investigated. It is shown, that under a well-spread condition on the…

Probability · Mathematics 2016-08-30 Gilles Bonnet , Pierre Calka , Matthias Reitzner

We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, the oscillation of the logarithm of the interior and exterior…

Classical Analysis and ODEs · Mathematics 2020-11-11 Simon Bortz , Max Engelstein , Max Goering , Tatiana Toro , Zihui Zhao

We present a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz. More precisely, we establish scale invariant absolute continuity of harmonic measure with respect to surface measure, along with higher…

Classical Analysis and ODEs · Mathematics 2015-07-09 Steve Hofmann , José María Martell

Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we…

Mathematical Physics · Physics 2015-05-13 Nick Laskin

We study percolation in the following random environment: let $Z$ be a Poisson process of constant intensity in the plane, and form the Voronoi tessellation of the plane with respect to $Z$. Colour each Voronoi cell black with probability…

Probability · Mathematics 2007-05-23 Bela Bollobas , Oliver Riordan

In this paper we introduce, via a Phragmen-Lindel\"of type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the {\sl pluricomplex Poisson kernel} because it shares many properties with…

Complex Variables · Mathematics 2020-12-02 Filippo Bracci , Alberto Saracco , Stefano Trapani

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…

Statistical Mechanics · Physics 2016-07-25 Coline Larmier , Eric Dumonteil , Fausto Malvagi , Alain Mazzolo , Andrea Zoia

In this paper, we characterize the class of distributions on an homogeneous Lie group $\fN$ that can be extended via Poisson integration to a solvable one-dimensional extension $\fS$ of $\fN$. To do so, we introducte the $\ss'$-convolution…

Classical Analysis and ODEs · Mathematics 2009-09-02 Ewa Damek , Jacek Dziubanski , Philippe Jaming , Salvador Pérez-Esteva

In the algebra Sym(gl(m)) we consider Poisson pencils generated by the linear Poisson-Lie bracket {,}_{gl(m)} and that corresponding to the so-called Reflection Equation Algebra. Each bracket of such a pencil has the Poisson center…

Quantum Algebra · Mathematics 2010-02-09 D. I. Gurevich , P. A. Saponov

In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method from [4], we obtain the Laplace domain expressions of the…

Classical Analysis and ODEs · Mathematics 2024-08-09 Hendrik De Bie , Ze Yang

A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{\alpha, \beta}(\lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that…

Statistics Theory · Mathematics 2018-02-23 Richard Herrmann

In a previous work, two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane…

Probability · Mathematics 2009-05-29 Pierre Calka , Julien Michel , Katy Paroux

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Statistics Theory · Mathematics 2015-10-02 Piero Barone

Carlitz [2] initiated a study on degenerate versions of Bernoulli and Euler numbers which has been extended recently to the researches on various degenerate versions of quite a few special numbers and polynomials. They have been explored by…

Number Theory · Mathematics 2021-06-28 Taekyun Kim , Dae san Kim , Hyunseok Lee , Seong Ho Park , Jongkyum Kwon

We provide a simple method for obtain boundary asymptotics of the Poisson kernel on a domain in $\RR^N$.

Complex Variables · Mathematics 2007-05-23 Steven G. Krantz

In this paper we study associative algebras with a Poisson algebra structure on the center acting by derivations on the rest of the algebra. These structures, which we call Poisson fibred algebras, appear in the study of quantum groups at…

q-alg · Mathematics 2008-02-03 Nicolai Reshetikhin , Alexander A. Voronov , Alan Weinstein

In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function {\alpha}. The affinity function {\alpha} measures the similarity between points in…

Classical Analysis and ODEs · Mathematics 2013-07-15 Ronald R. Coifman , Matthew J. Hirn

Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…

Mathematical Physics · Physics 2014-08-18 David Aristoff

The purpose of the paper is to provide a general method for computing hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2\Delta + F\cdot\nabla, with F bounded and orthogonal to the boundary…

Probability · Mathematics 2011-11-04 Tomasz Byczkowski , Jakub Chorowski , Piotr Graczyk , Jacek Malecki

For a hyperbolic Brownian motion on the Poincar\'e half-plane $\mathbb{H}^2$, starting from a point of hyperbolic coordinates $z=(\eta, \alpha)$ inside a hyperbolic disc $U$ of radius $\bar{\eta}$, we obtain the probability of hitting the…

Probability · Mathematics 2018-01-09 Valentina Cammarota , Enzo Orsingher