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Anderson-like localization transition of random walks with resetting

Research output: Contribution to journalArticle

Original languageEnglish
Article number 053204
Number of pages28
JournalJournal of Statistical Mechanics: Theory and Experiment
DOIs
DateAccepted/In press - 2 Apr 2019
DatePublished (current) - 23 May 2019

Abstract

We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized phase settles above a critical resetting rate, or rate of memory use, and the probability density asymptotically adopts in this regime a non-equilibrium steady state similar to that of the well known problem of diffusion with resetting to the origin. The transition occurs because of the presence of a single impurity site where the resetting rate is lower than on other sites, and around which the walker spontaneously localizes. Near criticality, the localization length diverges with a critical exponent that falls in the same class as the self-consistent theory of Anderson localization of waves in random media. The critical dimensions are also the same in both problems. Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can be also useful for understanding spatial learning by living organisms.

    Research areas

  • random walks, resetting processes, non-Markov processes, non-equilibrium steady states, Anderson localization, critical exponents

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via IOP at https://iopscience.iop.org/article/10.1088/1742-5468/ab16c2. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 410 KB, PDF-document

    Embargo ends: 23/05/20

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    Licence: CC BY-NC-ND

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