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- W4301004232 abstract "The switch chain is a well-known Markov chain for sampling directed graphs with a given degree sequence. While not ergodic in general, we show that it is ergodic for regular degree sequences. We then prove that the switch chain is rapidly mixing for regular directed graphs of degree d, where d is any positive integer-valued function of the number of vertices. We bound the mixing time by bounding the eigenvalues of the chain. A new result is presented and applied to bound the smallest (most negative) eigenvalue. This result is a modification of a lemma by Diaconis and Stroock, and by using it we avoid working with a lazy chain. A multicommodity flow argument is used to bound the second-largest eigenvalue of the chain. This argument is based on the analysis of a related Markov chain for undirected regular graphs by Cooper, Dyer and Greenhill, but with significant extension required." @default.
- W4301004232 created "2022-10-04" @default.
- W4301004232 creator A5031194096 @default.
- W4301004232 date "2011-05-02" @default.
- W4301004232 modified "2023-09-28" @default.
- W4301004232 title "A polynomial bound on the mixing time of a Markov chain for sampling regular directed graphs" @default.
- W4301004232 doi "https://doi.org/10.48550/arxiv.1105.0457" @default.
- W4301004232 hasPublicationYear "2011" @default.
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