Optimal resetting strategies for search processes in heterogeneous environments

Abstract

In many physical situations, there appears the problem of reaching a single target that is spatially distributed. Here we analyse how stochastic resetting, also spatially distributed, can be used to improve the search process when the target location is quenched, i.e. it does not evolve in time. More specifically, we consider a model with minimal but sufficient ingredients that allows us to derive analytical results for the relevant physical quantities, such as the first passage time distribution. We focus on the minimisation of the mean first passage time and its fluctuations (standard deviation), which proves to be non-trivial. Our analysis shows that the no-disorder case is singular: for small disorder, the resetting rate distribution that minimises the mean first passage time leads to diverging fluctuations -- which impinge on the practicality of this minimisation. Interestingly, this issue is healed by minimising the fluctuations: the associated resetting rate distribution gives first passage times that are very close to the optimal ones.

26 pages, 9 figures

References in corpus (14)

• Theoretical perspective on the glass transition and amorphous materials
• Supercooled Liquids for Pedestrians
• Fractal free energy landscapes in structural glasses
• Diffusion with resetting in arbitrary spatial dimension
• Bidimensional intermittent search processes: an alternative to Levy flights strategies
• Intermittent random walks for an optimal search strategy: One-dimensional case
• First hitting times to intermittent targets
• Transient anomalous diffusion in heterogeneous media with stochastic resetting
• Work fluctuations for diffusion dynamics submitted to stochastic return
• Random walks on complex networks under node-dependent stochastic resetting
• Rate enhancement of gated drift-diffusion process by optimal resetting
• Introduction to the dynamics of disordered systems: equilibrium and gradient descent
• Information in feedback ratchets
• The high-d landscapes paradigm: spin-glasses, and beyond

Cited by in corpus (4)

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• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
• How target distributions shape optimal stochastic resetting
• On the optimal relaxation rate for the Metropolis algorithm in one dimension