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RANDOM PARKING, SEQUENTIAL ADSORPTION, AND THE JAMMING LIMIT

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By 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.