Anderson-like localization transition of random walks with resetting

Boyer, Denis; Falcón-Cortés, Andrea; Giuggioli, Luca; Majumdar, Satya N.

doi:10.1088/1742-5468/ab16c2

Cited by 26 publications

(21 citation statements)

References 56 publications

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“…While case iii) was originally found in [28] and later in [30], scalings iv) and iv) were found in [31] and, finally, all the asymptotic scalings derived herein were found in [29]. Likewise, transitions between different transport regimes have can possibly emerge as a consequence of spatial [46] or temporal [45] heterogeneities in the resetting process.…”

Section: Spatial Dispersal With Relocations To Visited Placessupporting

confidence: 55%

Anomalous Diffusion in Random-Walks With Memory-Induced Relocations

2019

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In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied during the last years as particular situations within a framework of random walks with memory. We focus on (i) stochastic motion with resets to its initial position followed by a waiting period, and (ii) diffusive motion with memory-driven relocations to previously visited positions. For both of them we show how the overall transport regime may be actively modified by the details of the relocation mechanism. arXiv:1910.09913v1 [cond-mat.stat-mech]

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Section: Spatial Dispersal With Relocations To Visited Placessupporting

confidence: 55%

Anomalous Diffusion in Random-Walks With Memory-Induced Relocations

2019

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“…In contrast, for r > r c (γ), the walker gets localised, i.e. p(n, t) becomes stationary at late times and the stationary distribution has an exponential tail with a characteristic localization length scale ξ(r) that diverges as one approaches the critical line as ξ (r − r c ) −ν where ν takes the same value as in the self-consistent theory of Anderson localization of waves in random media [146,147]. The critical value r c (γ) was shown to be related to the probability P no−return of no-return to the origin for the free random walker, i.e, without resetting, via the simple relation…”

Section: Localization-delocalization Transition Induced By Preferentimentioning

confidence: 99%

Stochastic resetting and applications

Evans

Majumdar

Schehr

2020

J. Phys. A: Math. Theor.

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In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.

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“…It was shown that the RWs perform slow sub-diffusion due to the dynamics of memory-driven resetting [61,62]. The model above was further studied in the presence of a single defect site where the RW stays with a finite probability [63,64]. Another discrete time RW on a lattice was considered in [65] where resetting with a probability relocated the walker to the previous maximum.…”

Section: Introductionmentioning

confidence: 99%

First passage under restart for discrete space and time: Application to one-dimensional confined lattice random walks

Bonomo

Pal

2021

Phys. Rev. E

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First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to outperform the completion of many first passage processes which otherwise would take longer time to finish. However, most of the studies so far assumed continuous time underlying first passage time processes and moreover considered continuous time resetting restricting out restart processes broken up into synchronized time steps. To bridge this gap, in this paper, we study discrete space and time first passage processes under discrete time resetting in a general set-up. We sketch out the steps to compute the moments and the probability density function which is often intractable in the continuous time restarted process. A criterion that dictates when restart remains beneficial is then derived. We apply our results to a symmetric and a biased random walker (RW) in one dimensional lattice confined within two absorbing boundaries. Numerical simulations are found to be in excellent agreement with the theoretical results. Our method can be useful to understand the effect of restart on the spatiotemporal dynamics of confined lattice random walks in arbitrary dimensions.

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Anderson-like localization transition of random walks with resetting

Cited by 26 publications

References 56 publications

Anomalous Diffusion in Random-Walks With Memory-Induced Relocations

Anomalous Diffusion in Random-Walks With Memory-Induced Relocations

Stochastic resetting and applications

First passage under restart for discrete space and time: Application to one-dimensional confined lattice random walks

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