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Sharpness of the phase transition for parking on random trees
Author(s) -
Contat Alice
Publication year - 2022
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.21061
Subject(s) - vertex (graph theory) , phase transition , random graph , statistical physics , mathematics , combinatorics , graph , random walk , tree (set theory) , physics , statistics , quantum mechanics
Recently, a phase transition phenomenon has been established for parking on random trees. We extend the results of Curien and Hénard on general Bienaymé–Galton–Watson trees and allow different car arrival distributions depending on the vertex outdegrees. We then prove that this phase transition is sharp by establishing a large deviations result for the flux of exiting cars. This has consequences on the offcritical geometry of clusters of parked spots which displays similarities with the classical Erdős–Renyi random graph model.