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November 2001 Saturation in a Makovian Parking Process
Raúl Gouet, F. Javier López
Ann. Appl. Probab. 11(4): 1116-1136 (November 2001). DOI: 10.1214/aoap/1015345397


We consider $\mathbb{Z}$ as an infinite lattice street where cars of integer length $m \geq 1$ can park. The parking process is described by a 0–1 interacting particle system such that a site $z \in \mathbb{Z}$ is in state 1 whenever a car has its rear end at z and 0 otherwise. Cars attempt to park after exponential times with parameter $\lambda$, leave after exponential times with parameter 1 and are not allowed to touch nor overlap. We define and study a jamming occupation density for this parking process, using the quasi-stationary distribution of a Markov chain related to the reversible measure of the particle system. An extension to a strip in $\mathbb{Z}^2$ is also investigated.


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Raúl Gouet. F. Javier López. "Saturation in a Makovian Parking Process." Ann. Appl. Probab. 11 (4) 1116 - 1136, November 2001.


Published: November 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1012.60087
MathSciNet: MR1878292
Digital Object Identifier: 10.1214/aoap/1015345397

Primary: 60K35
Secondary: 60K30

Keywords: interacting particle systems , Quasi-stationary distributions , Random parking

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 4 • November 2001
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