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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

The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…

Statistical Mechanics · Physics 2021-10-27 M. A. F. dos Santos , E. H. Colombo , C. Anteneodo

We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…

Statistical Mechanics · Physics 2019-11-05 Denis S. Grebenkov

We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…

Statistical Mechanics · Physics 2016-12-28 Adrian A. Budini

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…

Statistical Mechanics · Physics 2017-09-13 Stas Burov , Jae-Hyung Jeon , Ralf Metzler , Eli Barkai

Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…

Biological Physics · Physics 2019-05-30 Yann Lanoiselée , Denis S. Grebenkov

We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…

Soft Condensed Matter · Physics 2015-06-09 Gerald John Lapeyre

We discuss the situations under which Brownian yet non-Gaussian (BnG) diffusion can be observed in the model of a particle's motion in a random landscape of diffusion coefficients slowly varying in space. Our conclusion is that such…

Statistical Mechanics · Physics 2020-01-15 E. B. Postnikov , A. Chechkin , I. M. Sokolov

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…

Statistics Theory · Mathematics 2025-05-19 Yuzhong Cheng , Hiroki Masuda

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…

Disordered Systems and Neural Networks · Physics 2015-06-11 Yasmine Meroz , Igor M. Sokolov , Joseph Klafter

Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…

Statistical Mechanics · Physics 2015-06-19 Mykyta V. Chubynsky , Gary W. Slater

We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially-varying diffusivity $D(r)$, mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this…

Statistical Mechanics · Physics 2014-12-24 Andrey G. Cherstvy , Aleksei V. Chechkin , Ralf Metzler

Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in…

Statistical Mechanics · Physics 2026-03-18 Dan Shafir , Stanislav Burov

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…

Statistical Mechanics · Physics 2010-09-10 Alberto Saa , Roberto Venegeroles

Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…

Chaotic Dynamics · Physics 2019-05-01 Y. Sato , R. Klages

In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…

Statistical Mechanics · Physics 2020-08-05 Jakub Ślęzak , Stanislav Burov

We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…

Statistical Mechanics · Physics 2022-11-28 Gaia Pozzoli , Benjamin De Bruyne

We study generalised anomalous diffusion processes whose diffusion coefficient $D(x,t)\sim D_0|x|^{\alpha}t^{\beta}$ depends on both the position $x$ of the test particle and the process time $t$. This process thus combines the features of…

Statistical Mechanics · Physics 2015-02-06 Andrey G. Cherstvy , Ralf Metzler

We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments…

Statistical Mechanics · Physics 2016-12-14 Daniel Molina-García , Tuan Minh Pham , Paolo Paradisi , Carlo Manzo , Gianni Pagnini

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…

Statistical Mechanics · Physics 2025-03-19 Pyei Phyo Lin , Matthias Wächter , Joachim Peinke , M. Reza Rahimi Tabar