Related papers: Recent Developments on the Moment Problem
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to determine the collisional moments of second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample, since we do not have a sample from the target. These and other considerations motivate the…
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…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
Classical results of Stieltjes are used to obtain explicit formulas for the peakon-antipeakon solutions of the Camassa-Holm equation. The closed form solution is expressed in terms of the orthogonal polynomials of the related classical…
We compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…
We investigate the impact of momentum-dependent relaxation time approximation in the Boltzmann equation within the Bjorken flow framework by analyzing the moments of the single-particle distribution function. The moment equations, which…
A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established.…
Evolution of a multiplicity distribution can be described with the help of master equation. We first look at 3rd and 4th factorial moments of multiplicity distributions and derive their equilibrium values. From them central moments and…
In this paper we study the distribution tails and the moments of a condition number which arises in the study of homogeneous systems of linear inequalities. We consider the case where this system is defined by a Gaussian random matrix and…
We solve the moment problem for convex distribution functions on $[0,1]$ in terms of completely alternating sequences. This complements a recent solution of this problem by Diaconis and Freedman, and relates this work to the…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
We find necessary and sufficient conditions for the existence of a probability measure on $\mathbb{N}_0$, the nonnegative integers, whose first $n$ moments are a given $n$-tuple of nonnegative real numbers. The results, based on finding an…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
Assuming the Generalized Riemann Hypothesis and the Generalized Ramanujan Conjecture, we determine the order of the $2(k_1,\dots,k_r)$th moment of a product of distinct irreducible $L$-functions on the critical line. As a consequence, we…
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density…