Median and Mode in First Passage under Restart

Abstract

Restart -- interrupting a stochastic process followed by a new start -- is known to improve the mean time to its completion, and the general conditions under which such an improvement is achieved are now well understood. Here, we explore how restart affects other important metrics of first-passage phenomena, namely the median and the mode of the first-passage time distribution. Our analysis provides a general criterion for when restart lowers the median time, and demonstrates that restarting is always helpful in reducing the mode. Additionally, we show that simple non-uniform restart strategies allow to optimize the mean and the median first-passage times, regardless of the characteristic time scales of the underlying process. These findings are illustrated with the canonical example of a diffusive search with resetting.

arXiv comment5 pages, 5 figures

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• The inspection paradox in stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Mean-performance of sharp restart I: Statistical roadmap
• Diffusion with Local Resetting and Exclusion
• Diffusion with two resetting points
• Tail-behavior roadmap for sharp restart
• Optimal Measurement Protocols in Quantum Zeno Effect
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Universal performance bounds of restart