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Parking on a random tree

Abstract:

Consider a uniform random rooted labelled tree on n vertices. We imagine that each node of the tree has space for a single car to park. A number m ≤ n of cars arrive one by one, each at a node chosen independently and uniformly at random. If a car arrives at a space which is already occupied, it follows the unique path towards the root until it encounters an empty space, in which case it parks there; if there is no empty space, it leaves the tree. Consider m = ⌊α n⌋ and let An,α denote the ev...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1017/S0963548318000457

Authors


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Institution:
University of Oxford
Division:
MPLS Division
Department:
Statistics
Oxford college:
Lady Margaret Hall
Role:
Author
ORCID:
0000-0003-2750-6848
Publisher:
Cambridge University Press Publisher's website
Journal:
Combinatorics, Probability and Computing Journal website
Volume:
28
Issue:
1
Pages:
23-45
Publication date:
2018-10-23
Acceptance date:
2018-08-01
DOI:
EISSN:
1469-2163
ISSN:
0963-5483
Pubs id:
pubs:870372
URN:
uri:0897bfee-1e40-46b3-9042-ea00da728b91
UUID:
uuid:0897bfee-1e40-46b3-9042-ea00da728b91
Local pid:
pubs:870372

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