The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 29, Number 4 (2019), 2089-2113.
Parking on transitive unimodular graphs
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.
Ann. Appl. Probab., Volume 29, Number 4 (2019), 2089-2113.
Received: November 2017
Revised: October 2018
First available in Project Euclid: 23 July 2019
Permanent link to this document
Digital Object Identifier
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)
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. https://projecteuclid.org/euclid.aoap/1563869038