Diffusion under time-dependent resetting

Abstract

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. Finally we consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time. We study optimal properties of the mean first passage time and show that a threshold function is at least locally optimal for the problem of minimizing the mean first passage time.

15 pages, 4 figures

References in corpus (12)

• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion in a potential landscape with stochastic resetting
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Random walks with preferential relocations to places visited in the past and their application to biology
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Fluctuating interfaces subject to stochastic resetting
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• Monotonous continuous-time random walks with drift and stochastic reset events
• Large deviations for Markov processes with resetting
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Random walk with random resetting to the maximum
• Optimization and universality of Brownian search in quenched heterogeneous media

Cited by in corpus (167)

• Stochastic Resetting and Applications
• First Passage Under Restart
• Experimental realization of diffusion with stochastic resetting
• 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
• Restart could optimize the probability of success in a Bernoulli trial
• 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
• Work fluctuations and Jarzynski equality in stochastic resetting
• Quantum dynamics with stochastic reset
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Diffusion with resetting in a logarithmic potential
• Landau theory of restart transitions
• Random walks on networks with stochastic resetting
• First passage under restart with branching
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Localization transition induced by learning in random searches
• Symmetric Exclusion Process under Stochastic Resetting
• Non-renewal resetting of scaled Brownian motion
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Stochastic resetting with stochastic returns using external trap
• Diffusion with stochastic resetting is invariant to return speed
• Ising model with stochastic resetting
• Transport properties and first arrival statistics of random searches with stochastic reset times
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Transport properties of random walks under stochastic non-instantaneous resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• Invariants of motion with stochastic resetting and space-time coupled returns
• On subdiffusive continuous time random walks with stochastic resetting
• Long time scaling behaviour for diffusion with resetting and memory
• Continuous-time random walks with reset events: Historical background and new perspectives
• Intermittent resetting potentials
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Stochastic resetting by a random amplitude
• Extremal statistics for stochastic resetting systems
• Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity
• Entropy production in systems with unidirectional transitions
• Phase transitions in large deviations of reset processes
• Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting
• Space-dependent diffusion with stochastic resetting: A first-passage study
• Random acceleration process under stochastic resetting
• Record statistics for random walks and Lévy flights with resetting
• Resetting with stochastic return through linear confining potential
• Stochastic resetting on comb-like structures
• Continuous time random walks under power-law resetting
• Diffusive transport on networks with stochastic resetting to multiple nodes
• The cost of stochastic resetting
• First-passage Brownian functionals with stochastic resetting
• Number of distinct sites visited by a resetting random walker
• Continuous time random walks under Markovian resetting
• Diffusion with Partial Resetting
• First passage in the presence of stochastic resetting and a potential barrier
• Comparison of two models of tethered motion
• Mitigating long queues and waiting times with service resetting
• Resetting transition is governed by an interplay between thermal and potential energy
• Diffusion processes with Gamma-distributed resetting and non-instantaneous returns
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events
• Random walks on complex networks with first-passage resetting
• Mitigating long transient time in deterministic systems by resetting
• Universal framework for record ages under restart
• Thermodynamic cost of finite-time stochastic resetting
• Discrete space-time resetting model: Application to first-passage and transmission statistics
• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• Transient anomalous diffusion in heterogeneous media with stochastic resetting
• Stochastic resetting antiviral therapies prevents drug resistance development
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Brownian motion under non-instantaneous resetting in higher dimensions
• Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting
• Exact extreme, order and sum statistics in a class of strongly correlated system
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
• Random walks on complex networks under node-dependent stochastic resetting
• First detection probability in quantum resetting via random projective measurements
• Robust random search with scale-free stochastic resetting
• Anomalous diffusion in random-walks with memory-induced relocations
• Thermodynamic work of partial resetting
• Restart uncertainty relation for monitored quantum dynamics
• Resetting mediated navigation of active Brownian searcher in a homogeneous topography
• Random walks on complex networks under time-dependent stochastic resetting
• General approach to stochastic resetting
• Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon
• Dynamical phase transition in the first-passage probability of a Brownian motion
• Quantum resetting in continuous measurement induced dynamics of a qubit
• First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions
• Unusual stationary state in Brownian systems with Lorentz force
• Rate enhancement of gated drift-diffusion process by optimal resetting
• Dynamically emergent correlations between particles in a switching harmonic trap
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Diffusion with two resetting points
• Accumulation time of stochastic processes with resetting
• Instability in the quantum restart problem
• Random walks on complex networks with multiple resetting nodes: a renewal approach
• Median and Mode in First Passage under Restart
• Critical number of walkers for diffusive search processes with resetting
• Encounter-based approach to diffusion with resetting
• Random walks with stochastic resetting in complex networks: a discrete time approach
• Non-linear diffusion with stochastic resetting
• Striking universalities in stochastic resetting processes
• Stochastic resetting in the Kramers problem: A Monte Carlo approach
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Motion of a Brownian molecule in the presence of reactive boundaries
• Expediting Feller process with stochastic resetting
• Tail-behavior roadmap for sharp restart
• Tight-binding model subject to conditional resets at random times
• Random Search with Memory in Patchy Media: Exploration-Exploitation Tradeoff
• Capture of a diffusing lamb by a diffusing lion when both return home
• Non-Analytic Non-Equilibrium Field Theory: Stochastic Reheating of the Ising Model
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Optimizing Leapover Lengths of Lévy Flights with Resetting
• Optimal Measurement Protocols in Quantum Zeno Effect
• Effects of mortality on stochastic search processes with resetting
• Entropy rate of random walks on complex networks under stochastic resetting
• Measurement-induced resetting in open quantum systems
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Target Search Optimization by Threshold Resetting
• Queues with resetting: a perspective
• Resonances of recurrence time of monitored quantum walks
• Optimal conditions for first passage of jump processes with resetting
• Efficiency of a microscopic heat engine subjected to stochastic 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
• First passage in discrete-time absorbing Markov chains under stochastic resetting
• Manipulating phases in many-body interacting systems with subsystem resetting
• Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity
• Stochastic resetting prevails over sharp restart for broad target distributions
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Universal performance bounds of restart
• Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations
• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Random resetting in search problems
• Optimizing the random search of a finite-lived target by a Lévy flight
• Ratchet-mediated resetting: Current, efficiency, and exact solution
• Non-homogeneous random walks with stochastic resetting: an application to the Gillis model
• Entropy of Sharp Restart
• Mean first-encounter times of simultaneous random walkers with resetting on networks
• Crossover from Anomalous to Normal Diffusion: Ising Model with Stochastic Resetting
• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
• Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests
• Unified approach to reset processes and application to coupling between process and reset
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Stochastic Resetting Mitigates Latent Gradient Bias of SGD from Label Noise
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• The Pólya and Sisyphus lattice random walks with resetting -- a first passage under restart approach
• Continuous-Time Multi-Armed Bandits with Controlled Restarts
• Analytic and Monte Carlo Approximations to the Distribution of the First Passage Time of the Drifted Diffusion with Stochastic Resetting and Mixed Boundary Conditions
• Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting
• The distribution of the maximum of independent resetting Brownian motions
• Search of stochastically gated targets with diffusive particles under resetting
• Abrupt transitions in the optimization of diffusion with distributed resetting
• The one-dimensional telegraphic process with noninstantaneous stochastic resetting
• Gaussian Process and Levy Walk under Stochastic Non-instantaneous Resetting and Stochastic Rest
• Spikes in Poissonian quantum trajectories
• Arcsine laws for Brownian motion with Poissonian resetting
• An exactly solvable predator prey model with resetting
• Optimal detection of quantum states via projective measurements
• How target distributions shape optimal stochastic resetting
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting
• Designing non-equilibrium states of quantum matter through stochastic resetting