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

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 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 Erd\H{o}s et al. (2019). Our approach relies on an embedding argument, involving a Markov chain defined by Jerrum and Sinclair (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 (2017).

Speaker

Georgios Amanatidis, University of Essex

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk).