Exchangeable pairs from switchings

Details Exchangeable pairs from switchings Exchangeable pairs from switchings

2011-12-04

arxiv.org/abs/1112.0704v2

Mathematics

Combinatorics

Corrected typos and made other small changes; 16 pages

Scientific paper

The method of switchings is a technique for asymptotic enumeration, often applied to random regular graphs and other combinatorial structures. We demonstrate a strong link between switchings and Stein's method by applying a random switching to a random regular graph to construct an exchangeable pair. We use this idea to strengthen previous results on the distribution of cycles in random regular graphs, which allows us to calculate distributions of linear eigenvalue functionals of the adjacency matrices.

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