We establish some conditions on a regular bipartite graph G under
which the following holds: if M is an ergodic Markov chain on the set
of proper 3-colourings of G which updates the state of at most 10% of
the vertices of G at each step and whose stationary distribution is
uniform, then the mixing time of M is (essentially) exponential in the
size of the vertex set of G.

In particular, our result applies to Glauber dynamics for sampling uniformly
from the proper 3-colourings of the discrete hypercube.

Lecture #10815

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.

• 10815-10815-QuickTime.mov (568 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.

• 10815-10815-MPEG-1 DVD.mpg (677 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

• 10815-10815-DVD PCM Audio.aiff (495 MB - Audio Only)
• 10815-10815-MPEG-2 120min High Quality Encode.m2v (1128 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.