Coupling with the stationary distribution and improved sampling for colorings and independent sets

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dc.creatorHayes, Thomas P.
dc.creatorVigoda, Eric
dc.date2006-10-05
dc.date.accessioned2026-07-07T07:28:45Z
dc.date.available2026-07-07T07:28:45Z
dc.descriptionWe present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach. As an application, we show that for $k/Δ>1.764$, the Glauber dynamics on $k$-colorings of a graph on $n$ vertices with maximum degree $Δ$ converges in $O(n\log n)$ steps, assuming $Δ=Ω(\log n)$ and that the graph is triangle-free. Previously, girth $\ge 5$ was needed. As a second application, we give a polynomial-time algorithm for sampling weighted independent sets from the Gibbs distribution of the hard-core lattice gas model at fugacity $λ<(1-ε)e/Δ$, on a regular graph $G$ on $n$ vertices of degree $Δ=Ω(\log n)$ and girth $\ge 6$. The best known algorithm for general graphs currently assumes $λ<2/(Δ-2)$.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051606000000330 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0610188
dc.identifierhttp://arxiv.org/abs/math/0610188
dc.identifierAnnals of Applied Probability 2006, Vol. 16, No. 3, 1297-1318
dc.identifierdoi:10.1214/105051606000000330
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117849
dc.subjectProbability
dc.subject60J10 (Primary) 68W20 (Secondary)
dc.titleCoupling with the stationary distribution and improved sampling for colorings and independent sets
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