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Abstract
The largest components of the critical ErdösRényi graph, G(n,p) with p=1/n, have size of order n^{2/3} with high probability. We give detailed asymptotics for the probability that there is an unusually large component, i.e. of size an^{2/3} for large a. Our results, which extend work of Pittel, allow a to depend upon n and also hold for a range of values of p around 1/n. We also provide asymptotics for the distribution of the size of the component containing a particular vertex.
Original language  English 

Pages (fromto)  245271 
Number of pages  27 
Journal  Advances in Applied Probability 
Volume  50 
Issue number  1 
DOIs  
Publication status  Published  1 Mar 2018 
Keywords
 ErdosRényi
 component size
 critical window
 random graph
ASJC Scopus subject areas
 Statistics and Probability
 Applied Mathematics
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Dive into the research topics of 'The probability of unusually large components in the nearcritical ErdősRényi graph'. Together they form a unique fingerprint.Projects
 1 Finished

EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts
Engineering and Physical Sciences Research Council
3/04/13 → 2/07/16
Project: Research council