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We introduce multicritical Schur measures, which are probability laws oninteger partitions which give rise to non-generic fluctuations at their edge.They are in the same universality classes as one-dimensional momentum-spacemodels of free fermions in flat confining potentials, studied by Le Doussal,Majumdar and Schehr. These universality classes involve critical exponents ofthe form 1/(2m+1), with m a positive integer, and asymptotic distributionsgiven by Fredholm determinants constructed from higher order Airy kernels,extending the generic Tracy-Widom GUE distribution recovered for m=1. We alsocompute limit shapes for the multicritical Schur measures, discuss the finitetemperature setting, and exhibit an exact mapping to the multicritical unitarymatrix models previously encountered by Periwal and Shevitz.

Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution