Birds on a Wire

TL;DR

This paper studies the statistical behavior of birds landing on a wire, analyzing occupancy, gap distribution, and dynamics, with extensions and conjectures for higher-dimensional substrates.

Contribution

It provides a detailed analysis of bird landing dynamics on a wire and proposes conjectures for higher-dimensional cases, advancing understanding of spatial occupancy models.

Findings

Steady-state occupancy of the wire determined

Distribution of gaps between birds characterized

Conjectures proposed for higher-dimensional substrates

Abstract

We investigate the occupancy statistics of birds on a wire and on higher-dimensional substrates. In one dimension, birds land one by one on a wire and rest where they land. Whenever a newly arriving bird lands within a fixed distance of already resting birds, these resting birds immediately fly away. We determine the steady-state occupancy of the wire, the distribution of gaps between neighboring birds, and other basic statistical features of this process. We discuss conjectures for corresponding observables in higher dimensions.