Related papers: Time-dependent probability density functions and i…
The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of…
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…
We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm…
We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous and isotropic turbulent flows. We show that the probability density function…
Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of…
We describe the statistical properties of two large river systems: the Danube and the Mississippi. The properties of the two rivers are compared qualitatively to the general properties of a critical steady state system. Specifically, we…
Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future population. The accuracy of these models is often…
We investigate the behavior of dissipative particle dynamics (DPD) with time-correlated random noise. A new stochastic force for DPD is proposed which consists of a random force whose noise has an algebraic correlation proportional to 1/t…
The Velocity Gradients Technique (VGT) and the Probability Density Functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
Representing the parton distribution functions (PDFs) of the proton and other hadrons through flexible, high-fidelity parametrizations has been a long-standing goal of particle physics phenomenology. This is particularly true since the…
We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or…
We present a new calculation for the evolution of the 1-point Probability Distribution Function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman-Kolmogorov equation and second-order Eulerian…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast…
We consider strong approximations of $1+1$-dimensional stochastic PDEs driven by additive space-time white noise. It has been long proposed (Davie-Gaines '01, Jentzen-Kloeden '08), as well as observed in simulations, that approximation…
In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…