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.

arXiv comment26 pages, 9 figures

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Cited by in corpus (4)

• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• 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