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Starving Random Walks
- Publication Year :
- 2024
-
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 $\mathcal{S}$ steps. To address this problem, the key observable corresponds to the inter-visit time $\tau_k$ defined as the time elapsed between the finding of the $k^\text{th}$ and the $(k+1)^\text{th}$ food unit. By characterizing the maximum $M_n$ of the inter-visit times $\tau_0,\dots,\tau_{n-1}$, we will see how to obtain the number $N_\mathcal{S}$ of food units collected at starvation, as well as the lifetime $T_\mathcal{S}$ of the starving RW.<br />Comment: 21 pages, 5 figures. Contribution to the book "The Mathematics of Movement: an Interdisciplinary Approach to Mutual Challenges in Animal Ecology and Cell Biology" edited by Luca Giuggioli and Philip Maini
- Subjects :
- Condensed Matter - Statistical Mechanics
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.14248
- Document Type :
- Working Paper