Asymptotics in Knuth's parking problem for caravans

Authors :: Jean Bertoin
Grégory Miermont
University of Zurich
Miermont, G
Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Laboratoire de Mathématiques d'Orsay (LM-Orsay)
Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
Benassù, Serena
Source :: Random Structures and Algorithms, Random Structures and Algorithms, 2006, 29 n.1, pp.38-55, Random Structures and Algorithms, Wiley, 2006, 29 (1), pp.38--55. ⟨10.1002/rsa.20092⟩, Random Structures and Algorithms, Wiley, 2006, 29 n.1, pp.38-55, Random Structures and Algorithms, 2006, 29 (1), pp.38--55. ⟨10.1002/rsa.20092⟩
Publication Year :: 2006
Abstract: 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.<br />Comment: 18 pages, 2 figures

Language :: English
ISSN :: 10429832 and 10982418
Database :: OpenAIRE
Journal :: Random Structures and Algorithms, Random Structures and Algorithms, 2006, 29 n.1, pp.38-55, Random Structures and Algorithms, Wiley, 2006, 29 (1), pp.38--55. ⟨10.1002/rsa.20092⟩, Random Structures and Algorithms, Wiley, 2006, 29 n.1, pp.38-55, Random Structures and Algorithms, 2006, 29 (1), pp.38--55. ⟨10.1002/rsa.20092⟩
Accession number :: edsair.doi.dedup.....afd3e279887555318ed7ebdee200c21f
Full Text :: https://doi.org/10.1002/rsa.20092⟩