Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting

Abstract

The strategy of stochastic resetting is known to expedite the first passage to a target, in diffusive systems. Consequently, the mean first passage time is minimized at an optimal resetting parameter. With Poisson resetting, vanishing transitions in the optimal resetting rate $r_{\ast }\to 0$ (continuously or discontinuously) have been found for various model systems, under the further influence of an external potential. In this paper, we explore how the discontinuous transitions in this context are regulated by two other factors -- the first one is spatial dimensions within which the diffusion is embedded, and the second is the time delay introduced before restart. We investigate the effect of these factors by studying analytically two types of models, one with an ordinary drift and another with a barrier, and both types having two absorbing boundaries. In the case of barrier potential, we find that the effect of increasing dimensions on the transitions is quite the opposite of increasing refractory period.

References in corpus (20)

• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion in a potential landscape with stochastic 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
• Stochastic resetting: A (very) brief review
• Stochastic Search with Poisson and Deterministic Resetting
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Stochastic resetting in underdamped Brownian motion
• Extremal statistics for stochastic resetting systems
• Random acceleration process under stochastic resetting
• Resetting with stochastic return through linear confining potential
• First passage in the presence of stochastic resetting and a potential barrier
• Resetting transition is governed by an interplay between thermal and potential energy
• Stochastic resetting antiviral therapies prevents drug resistance development
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
• General approach to stochastic resetting
• Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias

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