The stable graph: The metric space scaling limit of a critical random graph with i.i.d. power-law degrees

Conchon--Kerjan, Guillaume; Goldschmidt, Christina

doi:10.1214/22-aop1587

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Cited by 10 publications

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“…However, different universality classes appear for the (unoriented) critical configuration model when the law of the degree sequence has a finite second moment but an infinite third moment and heavy tails. For example, if the degree distribution is such that the probability that a vertex has degree k is asymptotic to c • k −γ for some constant c > and some γ ∈ (3, 4), then the sizes of connected components are of order n (γ−2)/(γ−1) , see for example [6,12,17].…”

Section: Discussionmentioning

confidence: 99%

Sharpness of the phase transition for parking on random trees

Contat

2021

Random Struct Algorithms

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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.

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Section: Discussionmentioning

confidence: 99%