Stochastic Search with Poisson and Deterministic Resetting

Abstract

We investigate a stochastic search process in one, two, and three dimensions in which $N$ diffusing searchers that all start at $x_0$ seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate $r$, or deterministically, with a reset time $T$. In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large $N$, resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for $N$ searchers, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independent of $N$ over a suitable range of $N$. Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.

23 pages, 9 figures, IOP format. Revised version: figure added, introductory text added, references added, and various minor changes incorporated. V3: Final version to appear in JSTAT. A few more references added

References in corpus (22)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Diffusion with Optimal Resetting
• Optimal search strategies for hidden targets
• Optimal stochastic restart renders fluctuations in first passage times universal
• Diffusion in a potential landscape with stochastic resetting
• Random walks with preferential relocations to places visited in the past and their application to biology
• How do proteins search for their specific sites on coiled or globular DNA
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• Optimal first arrival times in Lévy flights with resetting
• Bidimensional intermittent search processes: an alternative to Levy flights strategies
• First passages in bounded domains: When is the mean first passage time meaningful?
• First passages for a search by a swarm of independent random searchers
• Monotonous continuous-time random walks with drift and stochastic reset events
• Mortality, Redundancy, and Diversity in Stochastic Search
• Random walk with random resetting to the maximum
• Phase transitions in optimal search times: how random walkers should combine resetting and flight scales
• Exploration and Trapping of Mortal Random Walkers
• Depletion-Controlled Starvation of a Diffusing Forager
• Optimal search strategies of space-time coupled random walkers with finite lifetimes
• Evanescent continuous time random walks

Cited by in corpus (90)

• Stochastic Resetting and Applications
• First Passage Under Restart
• Run and tumble particle under resetting: a renewal approach
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• First passage under stochastic resetting in an interval
• Stochastic resetting: A (very) brief review
• Search with home returns provides advantage under high uncertainty
• Resetting processes with non-instanteneous return
• The inspection paradox in stochastic resetting
• Scaled Brownian motion with renewal resetting
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Quantum dynamics with stochastic reset
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Diffusion with resetting in a logarithmic potential
• Optimization in First-Passage Resetting
• Landau theory of restart transitions
• Random walks on networks with stochastic resetting
• First passage under restart with branching
• Symmetric Exclusion Process under Stochastic Resetting
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Diffusion with stochastic resetting is invariant to return speed
• 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
• On subdiffusive continuous time random walks with stochastic resetting
• Stochastic resetting in underdamped Brownian motion
• Continuous-time random walks with reset events: Historical background and new perspectives
• Stochastic resetting in interacting particle systems: A review
• Stochastic resetting by a random amplitude
• Interacting Brownian Motion with Resetting
• Local time of diffusion with stochastic resetting
• Entropy production in systems with unidirectional transitions
• Space-dependent diffusion with stochastic resetting: A first-passage study
• Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting
• Record statistics for random walks and Lévy flights with resetting
• Resetting with stochastic return through linear confining potential
• Diffusive transport on networks with stochastic resetting to multiple nodes
• First-passage Brownian functionals with stochastic resetting
• Number of distinct sites visited by a resetting random walker
• Stochastic Resetting for Enhanced Sampling
• Diffusion with Partial Resetting
• First passage in the presence of stochastic resetting and a potential barrier
• Mean-performance of sharp restart I: Statistical roadmap
• Mitigating long queues and waiting times with service resetting
• Resetting transition is governed by an interplay between thermal and potential energy
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Exact Distributions of Currents and Frenesy for Markov Bridges
• Diffusion with Local Resetting and Exclusion
• Controlling particle currents with evaporation and resetting from an interval
• Mitigating long transient time in deterministic systems by resetting
• Transient anomalous diffusion in heterogeneous media with stochastic resetting
• Stochastic resetting antiviral therapies prevents drug resistance development
• Brownian motion under non-instantaneous resetting in higher dimensions
• Optimization and Growth in First-Passage Resetting
• Resetting mediated navigation of active Brownian searcher in a homogeneous topography
• Dynamical phase transition in the first-passage probability of a Brownian motion
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Diffusion with two resetting points
• Stochastic resetting in the Kramers problem: A Monte Carlo approach
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Non-linear diffusion with stochastic resetting
• Tail-behavior roadmap for sharp restart
• Expediting Feller process with stochastic resetting
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Exact distributions of cover times for $N$ independent random walkers in one dimension
• Fluctuations and first-passage properties of systems of Brownian particles with reset
• Capture of a diffusing lamb by a diffusing lion when both return home
• Effect of stochastic resetting on Brownian motion with stochastic diffusion coefficient
• Efficiency of random search with space-dependent diffusivity
• Diversity of Sharp Restart
• Effects of mortality on stochastic search processes with resetting
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Queues with resetting: a perspective
• Target Search Optimization by Threshold Resetting
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Stochastic resetting prevails over sharp restart for broad target distributions
• Optimizing the random search of a finite-lived target by a Lévy flight
• Entropy of Sharp Restart
• Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests
• Mean first-encounter times of simultaneous random walkers with resetting on networks
• The local principle of large deviations for compound Poisson process with catastrophes
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Local resetting with geometric confinement
• Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting
• The distribution of the maximum of independent resetting Brownian motions
• Chaotic resetting: A resetting strategy for deterministic chaotic systems
• Experimental evidence for strong emergent correlations between particles in a switching trap
• Inducing and optimizing Markovian Mpemba effect with stochastic reset