The shape of a memorised random walk

Michal Gnacik, Abdulrahman Alsolami, James Burridge

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We view random walks as the paths of foraging animals, perhaps searching for food or avoiding predators while forming a mental map of their surroundings. The formation of such maps requires them to memorise the locations they have visited. We model memory using a kernel, proportional to the number of locations recalled as a function of the time since they were first observed. We give exact analytic expressions relating the elongation of the memorised walk to the structure of the memory kernel, and confirm these by simulation. We find that more slowly decaying memories lead to less elongated mental maps.
Original languageEnglish
Article number083207
Number of pages26
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue numberAugust 2018
Publication statusPublished - 22 Aug 2018


  • Random Walk
  • Memory
  • Asphericity
  • Brownian Motion
  • Foraging


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