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The continuum limit of critical random graphs

Abstract:

We consider the Erdos-Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn -4/3, for some fixed λ ε ℝ. We prove that the sequence of connected components of G(n, p), considered as metric spaces using the graph distance rescaled by n -1/3, converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the theory of continuum random trees. Our result gives access to the answers to...

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Publisher copy:
10.1007/s00440-010-0325-4

Authors


Addario-Berry, L More by this author
Broutin, N More by this author
Goldschmidt, C More by this author
Journal:
Probability Theory and Related Fields
Volume:
152
Issue:
3-4
Pages:
367-406
Publication date:
2012-04-05
DOI:
ISSN:
0178-8051
URN:
uuid:99e46af1-9548-4ad5-ab33-2faa96c27065
Source identifiers:
321265
Local pid:
pubs:321265

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