From Alternating Sign Matrices to the Gaussian Unitary Ensemble

Abstract

The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the six-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian Unitary Ensemble and the GUE-corners process.

15 pages, 2 figures. v2: minor updates, to appear in Communications in Mathematical Physics

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• Arctic curves of the four-vertex model
• Domain wall fluctuations of the six-vertex model at the ice point