Recent progress in multi-type WR models

Add to your list(s) Download to your calendar using vCal

• Yuri Suhov (Cambridge & Sao Paulo)
• Tuesday 03 December 2013, 14:00-15:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

The q-type WR (Widom—Rowlinson) model describes q species of particles/cells in d dimensions, repelling each other when they belong to different species (a hard-core repulsion) and tolerating each other when they belong to the same species. For d at least 2 and q=2 (the original form of the model), if the densities of each type are high (and equal), the model is an example of non-uniqueness of shift-invariant ergodic Gibbs/DLR measures (Ruelle, 1972). Namely, there exist two such measures, they are generated by corresponding boundary conditions and are transformed into each other by interchanging the types of particles.

For larger values of q, the picture is more complicated and depends on the collection of hard-core repulsion diameters. In the talk, I’ll give a complete solution for q=3,4 and discuss conjectures for q at least 5. If the time permits, I’ll touch on quantum aspects of the problem.

This is a joint work with A. Mazel and I. Stuhl. No special preliminary knowledge is expected from the audience, either in Probability Theory or in Statistical Mechanics.

This talk is part of the Probability series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
• Probability
• School of Physical Sciences
• Statistical Laboratory info aggregator
• bld31

Note that ex-directory lists are not shown.