Persistence and first-passage properties in nonequilibrium systems

AJ Bray, SN Majumdar, G Schehr - Advances in Physics, 2013 - Taylor & Francis
In this review, we discuss the persistence and the related first-passage properties in
extended many-body nonequilibrium systems. Starting with simple systems with one or few …

Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

R Metzler, JH Jeon, AG Cherstvy… - Physical Chemistry …, 2014 - pubs.rsc.org
Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion

JH Jeon, AV Chechkin, R Metzler - Physical Chemistry Chemical …, 2014 - pubs.rsc.org
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian
process with a power-law time dependent diffusion coefficient. Its mean squared …

First exit times of harmonically trapped particles: a didactic review

DS Grebenkov - Journal of Physics A: Mathematical and …, 2014 - iopscience.iop.org
We revise the classical problem of characterizing first exit times of a harmonically trapped
particle whose motion is described by a one-or multidimensional Ornstein–Uhlenbeck …

First passage and first hitting times of Lévy flights and Lévy walks

VV Palyulin, G Blackburn, MA Lomholt… - New Journal of …, 2019 - iopscience.iop.org
For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-
passage and first-hitting (or first-arrival) times. These are, respectively, the times when the …

Spectral content of a single non-Brownian trajectory

D Krapf, N Lukat, E Marinari, R Metzler, G Oshanin… - Physical Review X, 2019 - APS
Time-dependent processes are often analyzed using the power spectral density (PSD)
calculated by taking an appropriate Fourier transform of individual trajectories and finding …

First passages in bounded domains: When is the mean first passage time meaningful?

TG Mattos, C Mejía-Monasterio, R Metzler… - Physical Review E …, 2012 - APS
We study the first passage statistics to adsorbing boundaries of a Brownian motion in
bounded two-dimensional domains of different shapes and configurations of the adsorbing …

Reflected fractional Brownian motion in one and higher dimensions

T Vojta, S Halladay, S Skinner, S Janušonis… - Physical Review E, 2020 - APS
Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic
process with long-ranged correlations, represents a widely applied, paradigmatic …

Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries

T Guggenberger, G Pagnini, T Vojta… - New Journal of …, 2019 - iopscience.iop.org
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-
time correlated increments and is frequently used to model anomalous diffusion processes …

Probability density of the fractional Langevin equation with reflecting walls

T Vojta, S Skinner, R Metzler - Physical Review E, 2019 - APS
We investigate anomalous diffusion processes governed by the fractional Langevin
equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As …