Universität zu Köln

Gracar, Peter ORCID: 0000-0001-8340-8340, Luechtrath, Lukas and Moerters, Peter (2021). PERCOLATION PHASE TRANSITION IN WEIGHT-DEPENDENT RANDOM CONNECTION MODELS. Adv. Appl. Probab., 53 (4). S. 1090 - 1115. SHEFFIELD: APPLIED PROBABILITY TRUST. ISSN 1475-6064

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Abstract

We investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gracar, Peter UNSPECIFIED orcid.org/0000-0001-8340-8340 UNSPECIFIED Luechtrath, Lukas UNSPECIFIED UNSPECIFIED UNSPECIFIED Moerters, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-564101
DOI:	10.1017/apr.2021.13
Journal or Publication Title:	Adv. Appl. Probab.
Volume:	53
Number:	4
Page Range:	S. 1090 - 1115
Date:	2021
Publisher:	APPLIED PROBABILITY TRUST
Place of Publication:	SHEFFIELD
ISSN:	1475-6064
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SUBCRITICAL REGIMES; CONTINUUM; LAWS Multiple languages Statistics & Probability Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/56410