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Critical random graphs: limiting constructions and distributional properties

Abstract:

We consider the Erdo{double acute}s-Rényi random graph G(n, p) inside the critical window, where p = 1/n + λn-4/3 for some λ ∈ R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n-1/3 and letting n → ∞ yields a non-trivial sequence of limit metric spaces C =(C1,C2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a s...

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Publication status:
Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Role:
Author
Journal:
ELECTRONIC JOURNAL OF PROBABILITY
Volume:
15
Pages:
741-775
Publication date:
2010-05-24
EISSN:
1083-6489
ISSN:
1083-6489
URN:
uuid:42075aee-d27b-4fc3-b7d2-c2153e8b6f1a
Source identifiers:
172671
Local pid:
pubs:172671

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