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 …

Restart could optimize the probability of success in a Bernoulli trial

S Belan - Physical review letters, 2018‏ - APS
The recently noticed ability of restart to reduce the expected completion time of first-passage
processes allows appealing opportunities for performance improvement in a variety of …

Stochastic search with Poisson and deterministic resetting

U Bhat, C De Bacco, S Redner - Journal of Statistical Mechanics …, 2016‏ - iopscience.iop.org
We investigate a stochastic search process in one, two, and three dimensions in which N
diffusing searchers that all start at x 0 seek a target at the origin. Each of the searchers is …

Mortality, redundancy, and diversity in stochastic search

B Meerson, S Redner - Physical review letters, 2015‏ - APS
We investigate a stochastic search process in one dimension under the competing roles of
mortality, redundancy, and diversity of the searchers. This picture represents a toy model for …

Phase transitions in optimal search times: How random walkers should combine resetting and flight scales

D Campos, V Méndez - Physical Review E, 2015‏ - APS
Recent works have explored the properties of Lévy flights with resetting in one-dimensional
domains and have reported the existence of phase transitions in the phase space of …

The escape problem for mortal walkers

DS Grebenkov, JF Rupprecht - The Journal of chemical physics, 2017‏ - pubs.aip.org
We introduce and investigate the escape problem for random walkers that may eventually
die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region …

Continuous-time random-walk model for anomalous diffusion in expanding media

F Le Vot, E Abad, SB Yuste - Physical Review E, 2017‏ - APS
Expanding media are typical in many different fields, eg, in biology and cosmology. In
general, a medium expansion (contraction) brings about dramatic changes in the behavior …

Slowest first passage times, redundancy, and menopause timing

SD Lawley, J Johnson - Journal of Mathematical Biology, 2023‏ - Springer
Biological events are often initiated when a random “searcher” finds a “target,” which is
called a first passage time (FPT). In some biological systems involving multiple searchers …

Heterogeneous continuous-time random walks

DS Grebenkov, L Tupikina - Physical Review E, 2018‏ - APS
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile
analytical formalism for studying and modeling diffusion processes in heterogeneous …

Constructing efficient strategies for the process optimization by restart

I Nikitin, S Belan - Physical Review E, 2024‏ - APS
Optimization of the mean completion time of random processes by restart is a subject of
active theoretical research in statistical physics and has long found practical application in …