Optimal Resetting Brownian Bridges via Enhanced Fluctuations – Archive ouverte HAL

Benjamin de Bruyne 1 Satya N. Majumdar 1 Gregory Schehr 2

Benjamin de Bruyne, Satya N. Majumdar, Gregory Schehr. Optimal Resetting Brownian Bridges via Enhanced Fluctuations. Physical Review Letters, American Physical Society, 2022. ⟨hal-03721523⟩

We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time $t_f$ is finite and the searcher returns to its starting point at $t_f$. This is simply a Brownian motion with a Poissonian resetting rate $r$ to the origin which is constrained to start and end at the origin at time $t_f$. We first provide a rejection-free algorithm to generate such resetting bridges in all dimensions by deriving an effective Langevin equation with an explicit space-time dependent drift $\tilde \mu({\bf x},t)$ and resetting rate $\tilde r({\bf x}, t)$. We also study the efficiency of the search process in one-dimension by computing exactly various observables such as the mean-square displacement, the hitting probability of a fixed target and the expected maximum. Surprisingly, we find that there exists an optimal resetting rate $r^*$ that maximizes the search efficiency, even in the presence of a bridge constraint. We show however that the physical mechanism responsible for this optimal resetting rate for bridges is entirely different from resetting Brownian motions without the bridge constraint.

  • 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. LPTHE – Laboratoire de Physique Théorique et Hautes Energies

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