Comparison of two models of tethered motion

Luca Giuggioli, Shamik Gupta, Matthew Chase

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

8 Citations (Scopus)
70 Downloads (Pure)


We consider a random walker whose motion is tethered around a focal
 point. We use two models that exhibit the same spatial dependence in the
 steady state but widely different dynamics. In one case, the walker is
 subject to a deterministic bias towards the focal point, while in the
 other case, it resets its position to the focal point at random times.
 The deterministic tendency of the biased walker makes the forays away
 from the focal point more unlikely when compared to the random nature of
 the returns of the resetting walker. This difference has consequences on
 the spatio-temporal dynamics at intermediate times. To show the
 differences in the two models, we analyze their probability distribution
 and their dynamics in presence and absence of partially or fully
 absorbing traps. We derive analytically various quantities: (i) mean
 first-passage times to one target, where we recover results obtained
 earlier by a different technique, (ii) splitting probabilities to either of two targets as well as survival probabilities when one or either target is partially absorbing. The interplay between confinement, diffusion and absorbing traps produces interesting non-monotonic effects in various quantities, all potentially accessible in experiments. The formalism developed here may have a diverse range of applications, from study of animals roaming within home ranges and of electronic excitations moving in organic crystals to developing efficient search algorithms for locating targets in a crowded environment.
Original languageEnglish
Article number075001
Number of pages15
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
Early online date17 Dec 2018
Publication statusPublished - 25 Jan 2019


  • Focal point model
  • Resetting model
  • Splitting probabilities
  • Transport processes


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