Related papers: A natural probability measure derived from Stern's…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
In the course of studies of the measure of chaos for the distribution of the prime numbers among the positive integers N arched structures have been found. It is given a brief description of the fine structure of the positive integers…
We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions, characterized by the location of the uniform distribution and the coupling parameter of the process,…
A natural unit interval order is a naturally labelled partially ordered set that avoids patterns ${\bf 3} + {\bf 1}$ and $\bf 2 + 2$. To each natural unit interval order one can associate a symmetric function. The Stanley-Stembridge…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical…
We show that there exists a unique (up to multiplication by constants) and natural measure on simple loops in the plane and on each Riemann surface, such that the measure is conformally invariant and also invariant under restriction (i.e.…
We present a novel technique to parametrize experimental data, based on the construction of a probability measure in the space of functions, which retains the full experimental information on errors and correlations. This measure is…
We present a radically new proposal for the solution of the naturalness/hierarchy problem, where the fine-tuning of the Higgs mass finds its physical explanation and the well-known multiplicative renormalization of the usual perturbative…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As…
We obtain a complete description for a probability measure to be doubling on an arbitrarily given uniform Cantor set. The question of which doubling measures on such a Cantor set can be extended to a doubling measure on [0; 1] is also…
We determine the probability distribution for relative projective objects in an exceptional sequence of type $A_n$ of any length. We show that these events (the $j$-th object in an exceptional sequence of length $k\le n$ being relatively…
It is shown that the inert properties of a stationary random process can be expressed in terms of the ratio of its correlation interval to the doubled variance. When using a fixed value of the Planck constant h as a proportionality factor,…
Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this…