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Phase Uniqueness for the Mallows Model

Mathematical Physics & Probability

Speaker: Shannon Starr, University of Alabama at Birmingham
Location: 2112 MSB
Start time: Tue, Nov 24 2015, 2:10PM

A simple mean-field Hamiltonian for spins in R^2 is: h((x(i),y(i)),(x(j),y(j))) is equal to 1 if the slope of the line segment joining (x(i),y(i)) to (x(j),y(j)) is negative, and 0 otherwise. This leads to a Gibbs measure called the Mallows measure on permutations. If one scales the inverse-temperature beta with the number of particles in a certain way, then one obtains a limit called the "Frank copula." With Meg Walters we studied the large deviation principle for the Mallows measure, which can be used to prove uniqueness of the equilibrium measures. It might also be a good alternative to the Frank copula ldp.