From Alternating Sign Matrices to the Gaussian Unitary Ensemble
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The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the 6-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian Unitary Ensemble and the GUE-corners process.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Mathematical Physics
Springer Berlin Heidelberg
Gorin, Vadim. “From Alternating Sign Matrices to the Gaussian Unitary Ensemble.” Communications in Mathematical Physics 332.1 (2014): 437–447.
Author's final manuscript