Localization Transition Induced by Learning in Random Searches

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

Research output: Contribution to journalArticle (Academic Journal)peer-review

56 Citations (Scopus)
414 Downloads (Pure)


We solve an adaptive search model where a random walker or Lévy flight stochastically resets to previously visited sites on a d-dimensional lattice containing one trapping site. Because of reinforcement, a phase transition occurs when the resetting rate crosses a threshold above which nondiffusive stationary states emerge, localized around the inhomogeneity. The threshold depends on the trapping strength and on the walker’s return probability in the memoryless case. The transition belongs to the same class as the self-consistent theory of Anderson localization. These results show that similarly to many living organisms and unlike the well-studied Markovian walks, non-Markov movement processes can allow agents to learn about their environment and promise to bring adaptive solutions in search tasks.
Original languageEnglish
Article number40603
Number of pages6
JournalPhysical Review Letters
Issue number14
Early online date4 Oct 2017
Publication statusPublished - 6 Oct 2017

Structured keywords

  • Engineering Mathematics Research Group


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