Abrupt transitions in the optimization of diffusion with distributed resetting

Abstract

Brownian diffusion subject to stochastic resetting to a fixed position has been widely studied for applications to random search processes. In an unbounded domain, the mean first-passage time at a target site can be minimized for a convenient choice of the resetting rate. Here we study this optimization problem in one dimension when resetting occurs to random positions, chosen from a probability density function with compact support that does not include the target. Depending on the shape of this distribution, the optimal resetting rate either varies smoothly with the mean distance to the target, as in single-site resetting, or exhibits a discontinuity caused by the presence of a second local minimum in the mean first-passage time. These two regimes are separated by a critical line containing a singular point that we characterize through a Ginzburg-Landau theory. To quantify how useful is a given resetting point for the search, we calculate the probability density function of the last resetting position before absorption. The discontinuous transition separates two markedly different optimal strategies: one with a small resetting rate where the last path before absorption starts from a rather distant but likely position, while the other strategy has a large resetting rate, favoring last paths starting from not-so-likely points but which are closer to the target.

11 pages, 5 Figures

References in corpus (33)

• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• 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
• Stochastic resetting in backtrack recovery by RNA polymerases
• First passage under stochastic resetting in an interval
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• Optimal first arrival times in Lévy flights with resetting
• Google matrix analysis of directed networks
• Search with home returns provides advantage under high uncertainty
• Effects of refractory period on stochastic resetting
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Landau theory of restart transitions
• On subdiffusive continuous time random walks with stochastic resetting
• Restart expedites quantum walk hitting times
• Diffusive transport on networks with stochastic resetting to multiple nodes
• The cost of stochastic resetting
• Continuous time random walks under Markovian resetting
• Lotka-Volterra systems with stochastic resetting
• First passage in the presence of stochastic resetting and a potential barrier
• Comparison of two models of tethered motion
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events
• Thermodynamic cost of finite-time stochastic resetting
• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions
• Diffusion with two resetting points
• Instability in the quantum restart problem