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Multicritical random partitions

Authors
  • Betea, Dan
  • Bouttier, Jérémie
  • Walsh, Harriet
Publication Date
Dec 07, 2020
Source
Hal-Diderot
Keywords
Language
English
License
Unknown
External links

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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