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The Hagedorn transition as a Plancherel wall: Tracy-Widom statistics, Polyakov loops and partial deconfinement
We study the Hagedorn transition of the single-winding Dutta-Gopakumar unitary matrix model at finite rank $N$. Its Schur expansion is a sum of Plancherel probabilities restricted by the finite-rank wall on the number of rows, and the Vershik-Kerov-Logan-Shepp limit shape reaches this wall when the
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