Related papers: A nonlinear drift which leads to $\kappa$-generali…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…
Collisional thermalization of a particle ensemble under the energy dissipation can be seen in variety of systems, such as heated granular gasses and particles in plasmas. Despite its universal existence, analytical descriptions of the…
We study the discrete Fokker-Planck equation associated with the mean-field dynamics of a particle system called the dispersion process. For different regimes of the average number of particles per site (denoted by $\mu > 0$), we establish…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We introduce the $\alpha$-Gauss-Logistic map, a new nonlinear dynamics constructed by composing the logistic and $\alpha$-Gauss maps. Explicitly, our model is given by $x_{t+1} = f_L(x_t)x_t^{-\alpha} - \lfloor f_L(x_t)x_t^{-\alpha} \rfloor…
We present analytical results for the lowest cumulants of a stochastic process described by a Fokker-Planck equation with nonlinear drift. We show that, in the limit of small fluctuations, the mean, the variance and the covariance of the…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium…
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions…
This paper investigates the gradient flow structure, well-posedness, and asymptotic behavior of the Fokker-Planck equation defined on locally uniformly finite graphs, which is highly non-trivial compared with the finite case. We first…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations. As prototypes we study three variants of a…
We propose a novel mechanism for the origin of non-Gaussian tails in the probability distribution functions (PDFs) of local variables in nonlinear, diffusive, dynamical systems including passive scalars advected by chaotic velocity fields.…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of…
Transport processes in the fully ionized plasma with kappa-distribution and in strong magnetic field are studied. By analyzing the current density and the heat flux in the kappa-distributed plasma, we derive the corresponding transport…
The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck…