Capture of a diffusing lamb by a diffusing lion when both return home

R. K. Singh, Sadhana Singh

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A diffusing lion pursues a diffusing lamb when both of them are allowed to get back to their homes intermittently. Identifying the system with a pair of vicious random walkers, we study their dynamics under Poissonian and sharp resetting. In the absence of any resets, the location of intersection of the two walkers follows a Cauchy distribution. In the presence of resetting, the distribution of the location of annihilation is composed of two parts: one in which the trajectories cross without being reset (center) and the other where trajectories are reset at least once before they cross each other (tails). We find that the tail part decays exponentially for both the resetting protocols. The central part of the distribution, on the other hand, depends on the nature of the restart protocol, with Cauchy for Poisson resetting and Gaussian for sharp resetting. We find good agreement of the analytical results with numerical calculations.

Original languageEnglish
Article number064118
JournalPhysical Review E
Issue number6
StatePublished - 1 Dec 2022

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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