Séminaire Lotharingien de Combinatoire, 86B.49 (2022), 12 pp.
Dan Betea and Alessandra Occelli
Peaks of Cylindric Plane Partitions
Abstract.
We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic regimes depending on the trace/seam parameters, and in both cases we obtain asymptotics governed by finite temperature (periodic) analogues of the Bessel and Airy gap probabilities from random matrix theory. In particular, the distributions we obtain interpolate in more than one way between two well-known extremal value distributions: the Gumbel distribution of maxima of i.i.d. random variables and the Tracy-Widom distribution of maxima of eigenvalues of random Hermitian matrices. We also interpret our results in terms of last passage percolation on a cylinder, which yields interesting connections to the Kardar-Parisi-Zhang equation.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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