Critical number of walkers for diffusive search processes with resetting

Abstract

We consider $N$ Brownian motions diffusing independently on a line, starting at $x_0>0$, in the presence of an absorbing target at the origin. The walkers undergo stochastic resetting under two protocols: (A) each walker resets independently to $x_0$ with rate $r$ and (B) all walkers reset simultaneously to $x_0$ with rate $r$. We compute analytically the mean first-passage time to the origin and show that, as a function of $r$ and for fixed $x_0$, it has a minimum at an optimal value $r^{\ast }>0$ as long as $N<N_c$. Thus resetting is beneficial for the search for $N<N_c$. When $N>N_c$, the optimal value occurs at $r^{\ast }=0$ indicating that resetting hinders search processes. Continuing our results analytically to real $N$, we show that $N_c=7.3264773\dots$ for protocol A and $N_c=6.3555864\dots$ for protocol B, independently of $x_0$. Our theoretical predictions are verified in numerical Langevin simulations.

arXiv comment15 pages, 5 figures

References in corpus (27)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Stochastic Resetting and Applications
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Diffusion with Optimal Resetting
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal search strategies for hidden targets
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Diffusion with resetting in arbitrary spatial dimension
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• First passage under stochastic resetting in an interval
• Restart could optimize the probability of success in a Bernoulli trial
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Landau theory of restart transitions
• Phase transitions in optimal search times: how random walkers should combine resetting and flight scales
• Sisyphus random walk
• Long time scaling behaviour for diffusion with resetting and memory
• Intermittent resetting potentials
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Diffusive search for a stochastically-gated target with resetting
• Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
• Freezing transitions of Brownian particles in confining potentials

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• Dynamically emergent correlations between particles in a switching harmonic trap
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Target Search Optimization by Threshold Resetting
• Stochastic resetting prevails over sharp restart for broad target distributions
• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Optimizing the random search of a finite-lived target by a Lévy flight
• Mean first-encounter times of simultaneous random walkers with resetting on networks
• Diffusion with stochastic resetting on a lattice
• Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting
• The distribution of the maximum of independent resetting Brownian motions
• Experimental evidence for strong emergent correlations between particles in a switching trap