Universität zu Köln

Eckhoff, Maren, Moerters, Peter and Ortgiese, Marcel ORCID: 0000-0001-7803-8584 (2018). Near Critical Preferential Attachment Networks have Small Giant Components. J. Stat. Phys., 173 (3-4). S. 663 - 704. NEW YORK: SPRINGER. ISSN 1572-9613

Full text not available from this repository.

Abstract

Preferential attachment networks with power law exponent tau > 3 are known to exhibit a phase transition. There is a value rho(c) > 0 such that, for small edge densities rho <= rho(c) every component of the graph comprises an asymptotically vanishing proportion of vertices, while for large edge densities rho > rho(c) there is a unique giant component comprising an asymptotically positive proportion of vertices. In this paper we study the decay in the size of the giant component as the critical edge density is approached from above. We show that the size decays very rapidly, like exp(-c/root rho - rho(c)) for an explicit constant c > 0 depending on the model implementation. This result is in contrast to the behaviour of the class of rank-one models of scale-free networks, including the configuration model, where the decay is polynomial. Our proofs rely on the local neighbourhood approximations of Dereich and Morters (Ann Probab 41(1): 329-384, 2013) and recent progress in the theory of branching random walks (Gantert et al. in Ann Inst Henri Poincare Probab Stat 47(1): 111-129, 2011).

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Eckhoff, Maren UNSPECIFIED UNSPECIFIED UNSPECIFIED Moerters, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED Ortgiese, Marcel UNSPECIFIED orcid.org/0000-0001-7803-8584 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-167626
DOI:	10.1007/s10955-018-2054-5
Journal or Publication Title:	J. Stat. Phys.
Volume:	173
Number:	3-4
Page Range:	S. 663 - 704
Date:	2018
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1572-9613
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SURVIVAL PROBABILITY Multiple languages Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/16762