Communications in Mathematical Physics

, Volume 218, Issue 1, pp 153–176 | Cite as

Random Parking, Sequential Adsorption,¶and the Jamming Limit

  • Mathew D. Penrose


Identical cars are dropped sequentially from above into a large parking lot. Each car is positioned uniformly at random, subject to non-overlap with its predecessors, until jamming occurs. There have been many studies of the limiting mean coverage as the parking lot becomes large, but no complete proof that such a limit exists, until now.

We prove spatial laws of large numbers demonstrating that for various multidimensional random and cooperative sequential adsorption schemes such as the one above, the jamming limit coverage is well-defined.


Limit Coverage Complete Proof Sequential Adsorption Large Parking Random Parking 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mathew D. Penrose
    • 1
  1. 1.Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, UK. E-mail:

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