Starving Random Walks
L\'eo R\'egnier, Maxim Dolgushev, Olivier B\'enichou

TL;DR
This paper reviews recent findings on the starving random walk model, analyzing how resource-limited exploration affects the walker's lifetime and food collection based on inter-visit times and starvation thresholds.
Contribution
It introduces a framework to quantify the lifetime and food collection of starving random walks using inter-visit times and maximum inter-visit time analysis.
Findings
Characterization of inter-visit times and their maxima.
Relation between maximum inter-visit time and starvation lifetime.
Quantitative estimates of food units collected before starvation.
Abstract
In this chapter, we review recent results on the starving random walk (RW) problem, a minimal model for resource-limited exploration. Initially, each lattice site contains a single food unit, which is consumed upon visitation by the RW. The RW starves whenever it has not found any food unit within the previous steps. To address this problem, the key observable corresponds to the inter-visit time defined as the time elapsed between the finding of the and the food unit. By characterizing the maximum of the inter-visit times , we will see how to obtain the number of food units collected at starvation, as well as the lifetime of the starving RW.
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Taxonomy
TopicsDiffusion and Search Dynamics
