Random resetting in search problems

TL;DR

This paper reviews the theoretical foundations and practical applications of random resetting in search processes, demonstrating how resetting can improve efficiency across various stochastic models and real-world scenarios.

Contribution

It provides a comprehensive overview of the theoretical insights and criteria for effective resetting, along with diverse applications in fields like ecology, physics, and economics.

Findings

Resetting can significantly enhance search efficiency in stochastic processes.

Theoretical criteria determine when resetting improves search outcomes.

Applications span from animal foraging to ion transport and income dynamics.

Abstract

By periodically returning a search process to a known or random state, random resetting possesses the potential to unveil new trajectories, sidestep potential obstacles, and consequently enhance the efficiency of locating desired targets. In this chapter, we highlight the pivotal theoretical contributions that have enriched our understanding of random resetting within an abundance of stochastic processes, ranging from standard diffusion to its fractional counterpart. We also touch upon the general criteria required for resetting to improve the search process, particularly when distribution describing the time needed to reach the target is broader compared to a normal one. Building on this foundation, we delve into real-world applications where resetting optimizes the efficiency of reaching the desired outcome, spanning topics from home range search, ion transport to the intricate dynamics of income. Conclusively, the results presented in this chapter offer a cohesive perspective on the multifaceted influence of random resetting across diverse fields.