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CRITICAL PERCOLATION ON RANDOM REGULAR GRAPHS.
- Source :
-
Proceedings of the American Mathematical Society . Aug2018, Vol. 146 Issue 8, p3321-3332. 12p. - Publication Year :
- 2018
-
Abstract
- We show that for all d ∈ {3, . . .,n - 1} the size of the largest component of a random d-regular graph on n vertices around the percolation threshold p = 1/(d-1) is Θ(n2/3), with high probability. This extends known results for fixed d ≥ 3 and for d = n - 1, confirming a prediction of Nachmias and Peres on a question of Benjamini. As a corollary, for the largest component of the percolated random d-regular graph, we also determine the diameter and the mixing time of the lazy random walk. In contrast to previous approaches, our proof is based on a simple application of the switching method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 146
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 129689836
- Full Text :
- https://doi.org/10.1090/proc/14021