Abstract It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which still presented in its classical form modern reference works, valid if and only a certain parameter integer. In this light, it surprising much more powerful exists from the function , any real value parameter. greatly strengthens connections ...

In this paper, we study the statistical evolution of large-scale structure (LSS), focusing on joint probability distribution function (PDF) coarse-grained cosmic field and its role in constructing effective dynamics. As most comprehensive statistics, PDF encodes all cosmological information modes, therefore, could serve as basis LSS modelling. Following so-called PDF-based method from turbulenc...

This paper presents a model of the Stokes vector emission from the ocean surface. The ocean surface is described as an ensemble of facets with Cox and Munk’s Gram-Charlier slope distribution. The study discusses the impact of different up-wind and cross-wind rms slopes, skewness, peakedness, foam cover models and atmospheric effects on the azimuthal variation of the Stokes vector, as well as th...

We obtain orthogonal polynomial self-duality functions for multi-species version of the symmetric exclusion process (SEP$(2j)$) and independent random walker (IRW) on a finite undirected graph. In each process, we have $n>1$ species particles. addition, allow up to $2j$ particles occupy site in SEP$(2j)$. The duality SEP$(2j)$ IRW come from unitary intertwiners between different $*$-representat...

We propose a new formulation of the probability distribution function of wind driven water surface slope with an alpha-stable distribution probability. The mathematical formulation of the probability distribution function is given under an integral formulation. Application to represent the probability of time slope data from laboratory experiments is carried out with satisfactory results. We co...

In this paper, we consider the sequence (θn)n≥0 solving the Ramanujan equation en 2 = n ∑ k=0 nk k! + nn n! (θn − 1), n = 0, 1, . . . . The three main achievements are the following. We introduce a continuous– time extension θ(t) of θn and show its close connections with the medians λn of the Γ(n+1, 1) distributions and the Charlier polynomials. We give upper and lower bounds for both θ(t) and ...

Generally, blind separation of sources from their nonlinear mixtures is rather difficult. This nonlinear mapping, constituted by unsupervised linear mixing followed by unknown and invertible nonlinear distortion, is found in many signal processing cases. We propose using a kernel density estimator incorporated within an equivariant gradient algorithm to separate the nonlinear mixed sources. The...

The Pearcey process is a universal point in random matrix theory and depends on parameter [Formula: see text]. Let text] be the variable that counts number of points this fall interval In note, we establish following global rigidity upper bound: where arbitrary. We also obtain similar bound for maximum deviation points, central limit theorem individual fluctuations. proof short combines recent ...