The Annals of Applied Probability

Parking on transitive unimodular graphs

Michael Damron, Janko Gravner, Matthew Junge, Hanbaek Lyu, and David Sivakoff

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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 $p\geq1/2$, and only finitely many times otherwise.

Article information

Ann. Appl. Probab., Volume 29, Number 4 (2019), 2089-2113.

Received: November 2017
Revised: October 2018
First available in Project Euclid: 23 July 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 82B26: Phase transitions (general)

Annihilating particle system random walk blockades


Damron, Michael; Gravner, Janko; Junge, Matthew; Lyu, Hanbaek; Sivakoff, David. Parking on transitive unimodular graphs. Ann. Appl. Probab. 29 (2019), no. 4, 2089--2113. doi:10.1214/18-AAP1443.

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