Stochastic Resetting and Applications

Abstract

In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate $r$, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate $r$. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.

68 pages, Topical Review accepted version to appear in Journal of Physics A: Mathematical and Theoretical 2020

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• Enhancement of stability of metastable states in the presence of Lévy noise
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• Kinetic reconstruction of free energies as a function of multiple order parameters
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• Beyond the Big Jump: A Perturbative Approach to Stretched-Exponential Processes
• Semi-Markovian Dynamics of a Self-Propelled Particle in a Confined Environment: A Large-Deviation Study
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• Role of long jumps in Lévy noise induced multimodality
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• The one-dimensional telegraphic process with noninstantaneous stochastic resetting
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• Bounding energy growth in friction-less stochastic oscillators
• Physics of free climbing
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• Thermodynamic Cost of Random-Time Protocols
• Non-standard diffusion under Markovian resetting in bounded domains
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• Density-dependent stochastic resetting: a large deviations framework for achieving target distributions over networks
• Heterogeneous Mean First-Passage Time Scaling in Fractal Media
• Inducing and optimizing Markovian Mpemba effect with stochastic reset
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• Tethering effects on first-passage variables of lattice random walks in linear and quadratic focal point potentials
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• Interplay of noise induced stability and stochastic resetting
• Experimental evidence for strong emergent correlations between particles in a switching trap
• Extreme value statistics in a continuous time branching process: a pedagogical primer
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• An encounter-based approach for restricted diffusion with a gradient drift
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