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Phase Uniqueness for the Mallows Measure...
Starr, Shannon...

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Phase Uniqueness for the Mallows Measure on Permutations by Starr, Shannon ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
For a positive number $q$ the Mallows measure on the symmetric group is the probability measure on $S_n$ such that $P_{n,q}(\pi)$ is proportional to $q$-to-the-power-$\mathrm{inv}(\pi)$ where $\mathrm{inv}(\pi)$ equals the number of inversions: $\mathrm{inv}(\pi)$ 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 absence of phase transition, i.e., phase uniqueness.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.03727
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