Open Access
August 2019 Parking on transitive unimodular graphs
Michael Damron, Janko Gravner, Matthew Junge, Hanbaek Lyu, David Sivakoff
Ann. Appl. Probab. 29(4): 2089-2113 (August 2019). DOI: 10.1214/18-AAP1443


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.


Download Citation

Michael Damron. Janko Gravner. Matthew Junge. Hanbaek Lyu. David Sivakoff. "Parking on transitive unimodular graphs." Ann. Appl. Probab. 29 (4) 2089 - 2113, August 2019.


Received: 1 November 2017; Revised: 1 October 2018; Published: August 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07120704
MathSciNet: MR3983336
Digital Object Identifier: 10.1214/18-AAP1443

Primary: 60K35
Secondary: 82B26 , 82C22

Keywords: Annihilating particle system , blockades , Random walk

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 4 • August 2019
Back to Top