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Séminaire Lotharingien de Combinatoire, 85B.33 (2021), 12 pp.

# Dan Betea, Jérémie Bouttier and Harriet Walsh

# Multicritical Random Partitions

**Abstract.**
We study two families of probability measures on integer
partitions, which are Schur measures with parameters tuned in such a
way that the edge fluctuations are characterized by a critical
exponent different from the generic 1/3. We find that the first
part asymptotically follows a "higher-order analogue" of the
Tracy-Widom GUE distribution, previously
encountered by Le Doussal, Majumdar and Schehr in quantum
statistical physics. We also compute limit shapes, and discuss an
exact mapping between one of our families and the multicritical
unitary matrix models introduced by Periwal and Shevitz.

Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.

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