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arXiv · 1710.10529

Parking on transitive unimodular graphs

Michael Damron·Janko Gravner·Matthew Junge·Hanbaek Lyu·David Sivakoff
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Abstract

Place a car independently with probability $p$ at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot it parks there. Other cars can still drive over the site, but cannot park there. For a large class of transitive and unimodular graphs, we show that the root is almost surely visited infinitely many times when $p \geq 1/2$, and only finitely many times otherwise.

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Michael Damron, Janko Gravner, Matthew Junge, Hanbaek Lyu, David Sivakoff. 2017-10-28. Parking on transitive unimodular graphs. https://arxiv.org/abs/1710.10529

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