Multicritical random partitions. (English. French summary) Zbl 1502.60010
Summary: 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 P. Le Doussal et al. [“Multicritical edge statistics for the momenta of fermions in nonharmonic traps”, Phys. rev. Lett. 121, No. 3, Article ID 030603, 7 p. (2018; doi:10.1103/PhysRevLett.121.030603)] 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 V. Periwal and D. Shevitz [“Exactly solvable unitary matrix models: multicritical potentials and correlations”, Nucl. Phys. B 344, No. 3, 731–746 (1990; doi:10.1016/0550-3213(90)90676-5)].
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