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 (55)

• 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
• Run and tumble particle under resetting: a renewal approach
• 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 in backtrack recovery by RNA polymerases
• Diffusion with stochastic resetting at power-law times
• Fluctuating interfaces subject to stochastic resetting
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• Optimal first arrival times in Lévy flights with resetting
• Stochastic resetting: A (very) brief review
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Boosting search by rare events
• Stochastic Search with Poisson and Deterministic Resetting
• Search with home returns provides advantage under high uncertainty
• Restart could optimize the probability of success in a Bernoulli trial
• Large deviations for Markov processes with resetting
• Resetting processes with non-instanteneous return
• Effects of refractory period on stochastic resetting
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Single-molecule theory of enzymatic inhibition predicts the emergence of inhibitor-activator duality
• Diffusion with resetting in a logarithmic potential
• Landau theory of restart transitions
• Optimization in First-Passage Resetting
• First passage under restart with branching
• Non-renewal resetting of scaled Brownian motion
• Phase transitions in optimal search times: how random walkers should combine resetting and flight scales
• Diffusion with stochastic resetting is invariant to return speed
• Ising model with stochastic 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
• Invariants of motion with stochastic resetting and space-time coupled returns
• 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
• Diffusion with Resetting Inside a Circle
• First passage in the presence of stochastic resetting and a potential barrier
• Resetting transition is governed by an interplay between thermal and potential energy
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events
• 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
• Median and Mode in First Passage under Restart
• Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias

Cited by in corpus (3)

• Random resetting in search problems
• Power-law relaxation of a confined diffusing particle subject to resetting with memory
• Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling