Uittreksel
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-2 | Engels |
|---|---|
| Pagina's (van-tot) | 3-55 |
| Aantal pagina's | 53 |
| Tijdschrift | Random Structures and Algorithms |
| Volume | 55 |
| Nummer van het tijdschrift | 1 |
| DOI's | |
| Status | Gepubliceerd - aug 2019 |
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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 tijdschrift › Tijdschriftartikel › Academic › peer 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
PY - 2019/8
Y1 - 2019/8
N2 - 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.
AB - 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.
KW - percolation
KW - phase transition
KW - random graphs
KW - scaling window
UR - http://www.scopus.com/inward/record.url?scp=85060573432&partnerID=8YFLogxK
U2 - 10.1002/rsa.20837
DO - 10.1002/rsa.20837
M3 - Article
AN - SCOPUS:85060573432
VL - 55
SP - 3
EP - 55
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
SN - 1042-9832
IS - 1
ER -