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Exchangeable Pairs, Switchings, and Random Regular Graphs
We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the...
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Published in: | The Electronic journal of combinatorics 2015-02, Vol.22 (1) |
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Main Author: | |
Format: | Article |
Language: | English |
Citations: | Items that cite this one |
Online Access: | Get full text |
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Summary: | We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics for random regular graphs. Previous results on the distribution of cycle counts by McKay, Wormald, and Wysocka (2004) used the method of switchings, a combinatorial technique for asymptotic enumeration. Our proof uses Stein's method of exchangeable pairs and demonstrates an interesting connection between the two techniques. |
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ISSN: | 1077-8926 1077-8926 |
DOI: | 10.37236/4659 |