Related papers: Equilibrium problems for Raney densities

Motivated by a problem in the theory of integer-valued polynomials, we investigate the natural density of the solutions of equations of the form $\theta_uu_q(n)+\theta_ww_q(n)+\theta_2\frac{n(n+1)}{2}+\theta_1n+\theta_0\equiv 0\bmod d$,…

The application of control tools to complex flows frequently requires approximations, such as reduced-order models and/or simplified forcing assumptions, where these may be considered low-rank or defined in terms of simplified statistics…

We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining…

A previous study analyzed the convergence of probability densities for forward and inverse problems when a sequence of approximate maps between model inputs and outputs converges in $L^\infty$. This work generalizes the analysis to cases…

We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…

This article is dedicated to unifying the framework used to derive the Wiener--Hopf equations arising from some discrete and continuous wave diffraction problems.The main tools are the discrete Green's identity and the appropriate notion of…

We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…

We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…

This paper is the last of the series investigating renormalization group aspects of stochastic random matrices, including a Wigner-like disorder. We consider the equilibrium dynamics formalism that can be merged with the Ward identities…

To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…

We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a…

The weighted Delannoy numbers are defined by the recurrence relation $f_{m,n}=\alpha f_{m-1,n}+ \beta f_{m,n-1}+ \gamma f_{m-1,n-1}$ if $m n>0 $, with $f_{m,n}=\alpha^m \beta^n$ if $n m=0$. In this work, we study a generalization of these…

We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the classical case, we consider several generalizations in which the…

In this paper, we derive some new combinatorial inequalities by applying well known real analytic results like H\"{o}lder's inequality, Young's inequality, and Minkowiski's inequality to the recursively defined sequence $f_n$ of functions…

We provide new interpretations for a subset of Raney numbers, involving threshold sequences and Motzkin-like paths with long up and down steps. Given three integers n, k, l such that n >= 1, k >= 2 and 0 <= l <= k-2, a (k,l)-threshold…

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de…

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…

We introduce a pair of transformations, which are mutually inverse, acting on rather general classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as p-moments,…

We consider systems of stochastic fixed-point equations that arise in the asymptotic analysis of random recursive structures and algorithms such as Quicksort, generalized P\'olya urn processes and path lengths of random recursive trees and…