Related papers: Distributions in the constant-differentials P\'oly…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
Consider a P\'olya urn with balls of several colours, where balls are drawn sequentially and each drawn ball immediately is replaced together with a fixed number of balls of the same colour. It is well-known that the proportions of balls of…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
We derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form…
Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised…
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the…
A large number (~10,000) of uniform stainless steel balls comprising less than one layer coverage on a vertically shaken plate provides a rich system for the study of excited granular media. Viewed from above, the horizontal motion in the…
We study the angular process related to random walks in the Euclidean and in the non-Euclidean space where steps are Cauchy distributed. This leads to different types of non-linear transformations of Cauchy random variables which preserve…
We discuss the possibility of deriving an H-theorem for the nonlinear discrete time evolution known as Ulam's redistribution of energy problem. In this model particles are paired at random and then their total energy is redistributed…
Although the P\'olya enumeration theorem has been used extensively for decades, an optimized, purely numerical algorithm for calculating its coefficients is not readily available. We present such an algorithm for finding the number of…
Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles…
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 diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…
This is the second part of a two-part investigation. We continue the study of a class of balanced urn schemes on balls of two colors (white and black). At each drawing, a sample of size $m\ge 1$ is drawn from the urn and ball addition rules…
The static and the dynamic properties of a size-polydisperse model ionic liquid is studied using molecular dynamics simulations. Here, size of the anions is derived from a Gaussian distribution while keeping cation size fixed, resulting in…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
One way of defining probability distributions for circular variables (directions in two dimensions) is to radially project probability distributions, originally defined on $\mathbb{R}^2$, to the unit circle. Projected distributions have…