Component structure of the configuration model: barely supercritical case

Remco van der Hofstad, Svante Janson (Corresponding author), Malwina Luczak

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We study near-critical behavior in the configuration model. Let D n be the degree of a random vertex and (Formula presented.); we consider the barely supercritical regime, where ν n→1 as n→∞, but (Formula presented.). Let (Formula presented.) denote the size-biased version of D n. We prove that there is a unique giant component of size (Formula presented.), where ρ n denotes the survival probability of a branching process with offspring distribution (Formula presented.). This extends earlier results of Janson and Luczak, as well as those of Janson, Luczak, Windridge, and House, to the case where the third moment of D n is unbounded. We further study the size of the largest component in the critical regime, where (Formula presented.), extending and complementing results of Hatami and Molloy.

Originele taal-2Engels
Pagina's (van-tot)3-55
Aantal pagina's53
TijdschriftRandom Structures and Algorithms
Volume55
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - aug 2019

Vingerafdruk

Configuration
Model
Denote
Giant Component
Survival Probability
Branching process
Critical Behavior
Biased
Moment
Vertex of a graph

Citeer dit

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Component structure of the configuration model : barely supercritical case. / van der Hofstad, Remco; Janson, Svante (Corresponding author); Luczak, Malwina.

In: Random Structures and Algorithms, Vol. 55, Nr. 1, 08.2019, blz. 3-55.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - Component structure of the configuration model

T2 - barely supercritical case

AU - van der Hofstad, Remco

AU - Janson, Svante

AU - Luczak, Malwina

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