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.
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• HAL Id : hal-03043379, version 1
• ARXIV : 2012.01995

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Dan Betea, Jérémie Bouttier, Harriet Walsh. Multicritical random partitions. 33st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2021), Jan 2022, Ramat Gan, Israel. pp.#33. ⟨hal-03043379⟩

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