Asymptotics in Knuth's parking problem for caravans

Details Asymptotics in Knuth's parking problem for caravans Asymptotics in Knuth's parking problem for caravans

2005-02-10

arxiv.org/abs/math/0502220v1

Random Structures and Algorithms 29, 1 (2006) 38--55

Mathematics

Probability

18 pages, 2 figures

Scientific paper

10.1002/rsa.20092

We consider a generalized version of Knuth's parking problem, in which caravans consisting of a number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free space to park. Extending a recent work by Chassaing and Louchard, we relate the asymptotics for the sizes of blocks formed by occupied spots with the dynamics of the additive coalescent. According to the behavior of the caravan's size tail distribution, several qualitatively different versions of eternal additive coalescent are involved.

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