Phase Uniqueness for the Mallows Measure on Permutations

摘要: For a positive number $q$ the Mallows measure on symmetric group is probability $S_n$ such that $P_{n,q}(\pi)$ proportional to $q$-to-the-power-$\mathrm{inv}(\pi)$ where $\mathrm{inv}(\pi)$ equals of inversions: pairs $i \pi_j$. One may consider this as mean-field model from statistical mechanics. The weak large deviation principle replace Gibbs variational for characterizing equilibrium measures. In sense, we prove absence phase transition, i.e., uniqueness.