Random graph asymptotics on high-dimensional tori. II: volume, diameter and mixing time (Q639871)
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| English | Random graph asymptotics on high-dimensional tori. II: volume, diameter and mixing time |
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Random graph asymptotics on high-dimensional tori. II: volume, diameter and mixing time (English)
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11 October 2011
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The authors study critical bond-percolation on high-dimensional tori, removing a logarithmic correction in the lower bound considered in their previous paper [\textit{M. Heydenreich} and \textit{R. van der Hofstad}, Commun. Math. Phys. 270, No.~2, 335--358 (2007; Zbl 1128.82010)] and prove sharp lower bounds on the size of the largest cluster. The main result of the paper is that the behavior of the critical percolation on high-dimensional tori is the same as for critical Erdös-Rényi random graphs.
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percolation
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random graph asymptotics
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mean-field behavior
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critical window
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