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In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…

Statistics Theory · Mathematics 2023-05-10 Ali Zartash , Elina Robeva

Motivated by the study of H\"ormander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as…

Analysis of PDEs · Mathematics 2020-04-20 Iakovos Androulidakis , Omar Mohsen , Robert Yuncken

We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in…

Numerical Analysis · Mathematics 2024-11-14 Jean-François Coulombel , Grégory Faye

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…

Complex Variables · Mathematics 2022-10-25 Debraj Chakrabarti , Anirban Dawn

The paper deals with point-wise estimates for the heat kernel of a nonlocal convolution type operator with a kernel that decays at least exponentially at infinity. It is shown that the large time behaviour of the heat kernel depends…

Functional Analysis · Mathematics 2018-04-25 Alexander Grigoryan , Yury Kondratiev , Andrey Piatnitski , Elena Zhizhina

The notion of the H\"older convolution is introduced. The main result is that, under general conditions on functions L_1, ..., L_n, the function inverse to the Legendre--Fenchel transform of the H\"older convolution of L_1, ..., L_n…

Classical Analysis and ODEs · Mathematics 2013-06-04 Iosif Pinelis

The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical…

High Energy Physics - Theory · Physics 2014-11-20 Carl M. Bender , Daniel W. Hook , Peter N. Meisinger , Qing-hai Wang

In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of selfadjoint commuting random variables in an infinitesimal triangular array are…

Probability · Mathematics 2017-05-17 Takahiro Hasebe , Hao-Wei Huang , Jiun-Chau Wang

We study properties of an attractive-repulsive energy functional based on power-kernels, which can be used for halftoning of images. In the first part of this work, using a variational framework for probability measures, we examine…

Analysis of PDEs · Mathematics 2013-10-07 Jan-Christian Hütter

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

Probability · Mathematics 2015-03-18 Emmanuel Jacob , Peter Mörters

This paper deals with Student t-processes as studied in (Cufaro Petroni N 2007 J. Phys. A, Math. Theor. 40(10), 2227-2250). We prove and extend some conjectures expressed by Cufaro Petroni about the asymptotical behavior of a Student…

Probability · Mathematics 2009-11-13 C. Berg , C. Vignat

It is common knowledge that the Fourier transform enjoys the convolution property, i.e., it turns convolution in the time domain into multiplication in the frequency domain. It is probably less known that this property characterizes the…

Functional Analysis · Mathematics 2023-07-25 Mateusz Krukowski

Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lov\'asz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved…

Data Structures and Algorithms · Computer Science 2020-06-09 Sebastian Brandt , Christoph Grunau , Václav Rozhoň

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…

Probability · Mathematics 2017-05-03 Mokshay Madiman , James Melbourne , Peng Xu

We show that positive elements with respect to the twisted convolutions, belonging to some ultra-test function space of certain order at origin, belong to the ultra-test function space of the same order everywhere. We apply the result to…

Functional Analysis · Mathematics 2016-09-13 Yuanyuan Chen

We show two novel concentration inequalities for suprema of empirical processes when sampling without replacement, which both take the variance of the functions into account. While these inequalities may potentially have broad applications…

Machine Learning · Statistics 2014-11-27 Ilya Tolstikhin , Gilles Blanchard , Marius Kloft

We determine the distributional behavior for products of free random variables in a general infinitesimal triangular array. In the case of positive variables, the main theorem extends a result proved earlier for arrays with identically…

Operator Algebras · Mathematics 2007-05-23 Hari Bercovici , Jiun-Chau Wang

Recent progress on the understanding of the Random Conductance Model is reviewed. A particular emphasis is on homogenization results such as functional central limit theorems, local limit theorems and heat kernel estimates for almost every…

Probability · Mathematics 2025-04-10 Sebastian Andres

We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers with respect to free additive convolution and with…

Operator Algebras · Mathematics 2013-03-01 Michael Anshelevich , Serban T. Belinschi , Maxime Fevrier , Alexandru Nica

Fourier-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position…

High Energy Physics - Phenomenology · Physics 2016-07-20 Bertrand G. Giraud , Robi Peschanski