Birds on a wire

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.

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