Phase uniqueness for the Mallows measure on permutations

For a positive number q, the Mallows measure on the symmetric group is the probability measure on S-n such that P-n,P-q(pi) is proportional to q-to-the-power-inv(pi) where inv(pi) equals the number of inversions: inv(pi) equals the number of pairs i < j such that pi(i) > pi(j). One may consider this as a mean-field model from statistical mechanics. The weak large deviation principle may replace the Gibbs variational principle for characterizing equilibrium measures. In this sense, we prove the absence of phase transition, i.e., phase uniqueness. Published by AIP Publishing.