Yun Long, University of California, Berkeley, California, USA.Asaf Nachmias, University of British Columbia, Vancouver, Canada.Weiyang Ning, University of Washington, Seattle, USA.Yuval Peres, Microsoft Research, Redmond, Washington, USA.

• IntroductionStatement of the resultsMixing time preliminariesOutline of the proof of Theorem 2.1Random graph estimatesSupercritical caseSubcritical caseCritical caseFast mixing of the Swendsen-Wang process on treesAcknowledgementsBibliography

Yun Long, University of California, Berkeley, California, USA.Asaf Nachmias, University of British Columbia, Vancouver, Canada.Weiyang Ning, University of Washington, Seattle, USA.Yuval Peres, Microsoft Research, Redmond, Washington, USA.

• IntroductionStatement of the resultsMixing time preliminariesOutline of the proof of Theorem 2.1Random graph estimatesSupercritical caseSubcritical caseCritical caseFast mixing of the Swendsen-Wang process on treesAcknowledgementsBibliography

Yun Long, University of California, Berkeley, California, USA.Asaf Nachmias, University of British Columbia, Vancouver, Canada.Weiyang Ning, University of Washington, Seattle, USA.Yuval Peres, Microsoft Research, Redmond, Washington, USA.

• IntroductionStatement of the resultsMixing time preliminariesOutline of the proof of Theorem 2.1Random graph estimatesSupercritical caseSubcritical caseCritical caseFast mixing of the Swendsen-Wang process on treesAcknowledgementsBibliography