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Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We…

Statistical Mechanics · Physics 2009-11-07 Igor M. Sokolov , Ralf Metzler

The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…

Statistical Mechanics · Physics 2020-09-15 Maike A. F. dos Santos , Fernando D. Nobre , Evaldo M. F. Curado

We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ >…

Statistical Mechanics · Physics 2015-06-15 Andrey G. Cherstvy , Aleksei V. Chechkin , Ralf Metzler

In this paper we deal with high-order corrections for the Fractional Derivative approach to anomalous diffusion, in super-diffusive regime, which become relevand whenever one attempts to describe the behavior of particles close to normal…

Statistical Mechanics · Physics 2007-06-15 M. Marseguerra , A. Zoia

We use the two-time scale subordination in order to describe dynamical processes in continuous media with a long-term memory. Our consideration touches two physical examples in detail. First we study a temporal evolution of the species…

Statistical Mechanics · Physics 2011-11-15 Aleksander Stanislavsky , Karina Weron

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…

Biological Physics · Physics 2019-10-09 Nguiya P. Neo , Gary W. Slater

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…

Statistical Mechanics · Physics 2009-11-07 Govindan Rangarajan , Mingzhou Ding

We derive characteristic function identities for conditional distributions of an r-trimmed Levy process given its r largest jumps up to a designated time t. Assuming the underlying Levy process is in the domain of attraction of a stable…

Probability · Mathematics 2018-09-06 Yuguang F. Ipsen , Peter Kevei , Ross A. Maller

This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between…

Numerical Analysis · Mathematics 2024-05-30 Tan Zhang , Zhongjian Wang , Jack Xin , Zhiwen Zhang

We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…

Probability · Mathematics 2023-10-23 Mihail Bazhba , Jose Blanchet , Roger J. A. Laeven , Bert Zwart

We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil…

Statistical Mechanics · Physics 2023-09-01 Z. Tomovski , K. Gorska , T. Pietrzak , R. Metzler , T. Sandev

Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…

Statistical Mechanics · Physics 2016-07-06 Tomasz Srokowski

We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study…

Statistical Mechanics · Physics 2011-11-29 Vivien Lecomte , Uwe C. Tauber , Frederic van Wijland

We consider Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously in time, in order to study fluctuations of time-averaged observables in temporary heterogeneous diffusion…

Statistical Mechanics · Physics 2016-06-15 Takuma Akimoto , Eiji Yamamoto

We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…

Superconductivity · Physics 2009-10-31 D. A. Gorokhov , G. Blatter

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments of displacement, with exponents that do not depend linearly on the order of the moment. The exponents concerning small-order moments are dominated by…

Statistical Mechanics · Physics 2021-01-27 Jürgen Vollmer , Lamberto Rondoni , Muhammad Tayyab , Claudio Giberti , Carlos Mejía-Monasterio

Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…

Probability · Mathematics 2008-01-03 Rudolf Gorenflo , Entsar A. A. Abdel-Rehim

A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…

Statistical Mechanics · Physics 2025-07-24 Francisco J. Sevilla , Adriano Valdés-Gómez , Alexis Torres-Carbajal

In this paper, we consider an age-structured jump model that arises as a description of continuous time random walks with infinite mean waiting time between jumps. We prove that under a suitable rescaling, this equation converges in the…

Analysis of PDEs · Mathematics 2026-01-14 Hugues Berry , Pierre Gabriel , Thomas Lepoutre , Nathan Quiblier

The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…

Statistical Mechanics · Physics 2026-03-10 M. Süzen