Rapid mixing of the switch Markov chain for strongly stable degree sequences

The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show that the switch chain for sampling simple undirected graphs with a given degree sequence is rapidly mixing when the degree sequence...

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Vydáno v:Random structures & algorithms Ročník 57; číslo 3; s. 637 - 657
Hlavní autoři: Amanatidis, Georgios, Kleer, Pieter
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York John Wiley & Sons, Inc 01.10.2020
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Témata:
degree sequence
Graphs
Markov analysis
Markov chains
mixing time
Sampling
switch Markov chain
ISSN:1042-9832, 1098-2418
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Shrnutí:The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show that the switch chain for sampling simple undirected graphs with a given degree sequence is rapidly mixing when the degree sequence is so‐called strongly stable. Strong stability is satisfied by all degree sequences for which the switch chain was known to be rapidly mixing based on Sinclair's multicommodity flow method up until a recent manuscript of Erdős and coworkers in 2019. Our approach relies on an embedding argument, involving a Markov chain defined by Jerrum and Sinclair in 1990. This results in a much shorter proof that unifies (almost) all the rapid mixing results for the switch chain in the literature, and extends them up to sharp characterizations of P‐stable degree sequences. In particular, our work resolves an open problem posed by Greenhill and Sfragara in 2017.
Bibliografie:Funding information
This research was supported by the The Netherlands Organisation for Scientific Research Gravitation project NETWORKS, grant number 024.002.003.
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20949