Optimal first arrival times in L\'evy flights with resetting

TL;DR

This paper analyzes the mean first arrival time of a Le9vy flight with resetting, providing formulas and criteria for optimal search efficiency in super-diffusive motion.

Contribution

It introduces a formula for the MFAT in Le9vy flights with resetting and explores optimal resetting strategies for efficient target search.

Findings

Derived a formula for MFAT in Le9vy flights with resetting

Identified conditions for optimal resetting to minimize MFAT

Demonstrated super-diffusive motion leads to efficient search strategies

Abstract

We consider diffusive motion of a particle performing a random walk with L\'evy distributed jump lengths and subject to resetting mechanism bringing the walker to an initial position at uniformly distributed times. In the limit of infinite number of steps and for long times, the process converges to a super-diffusive motion with replenishment. We derive formula for a mean first arrival time (MFAT) to a predefined target position reached by a meandering particle and analyze efficiency of the proposed searching strategy by investigating criteria for an optimal (a shortest possible) MFAT.