Birds on a wire

Abstract

We investigate the occupancy statistics of birds on a wire. 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 briefly discuss conjectures for corresponding observables in higher dimensions.