We prove that the mixing time of any single-site dynamics on any bounded-degree
graph is at least $\Omega(n log n)$. The result holds for arbitrary spin systems,
including those with hard constraints such as colorings and the hard-core model.
One corollary is that many $O(n log n)$ mixing time results in the literature are
in fact optimal. This had been known previously only in very restricted cases,
such as completely independent spins and one-dimensional systems. The main techniques
used in the proof are disagreement percolation and monotonicity properties of the
dynamics.

Joint work with Alistair Sinclair

Lecture #10796

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 10796-10796-QuickTime.mov (447 MB)

Download MPEG File

You can download the MPEG file here. Right click on the link and "Save As..." to save to your local computer.

• 10796-10796-MPEG-1 DVD.mpg (604 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 10796-10796-DVD PCM Audio.aiff (442 MB - Audio Only)
• 10796-10796-MPEG-2 120min High Quality Encode.m2v (1007 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.