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- W4301112295 abstract "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 functionals 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." @default.
- W4301112295 created "2022-10-04" @default.
- W4301112295 creator A5068921142 @default.
- W4301112295 date "2011-12-03" @default.
- W4301112295 modified "2023-09-28" @default.
- W4301112295 title "Exchangeable pairs, switchings, and random regular graphs" @default.
- W4301112295 doi "https://doi.org/10.48550/arxiv.1112.0704" @default.
- W4301112295 hasPublicationYear "2011" @default.
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