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.

arXiv comment12 pages, 3 figures (v2: minor modifications and clarifications). Extended abstract for FPSAC 2021

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• Multicritical edge statistics for the momenta of fermions in non-harmonic traps
• The periodic Schur process and free fermions at finite temperature
• Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes

Cited by in corpus (3)

• Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
• Interface fluctuations associated with split Fermi seas
• Classical group matrix models and universal criticality