We study the emptiness formation probability (EFP) in the six-vertex
model with domain wall boundary conditions. At the ice point, i.e.,
when all the Boltzmann weights are equal, we are able to build an explicit,
although still conjectural, expression for the EFP in terms of a finite-size
matrix determinant of Fredholm type. The obtained representation can
be further written as the Fredholm determinant of some linear integral operator.
As the geometric parameters of the EFP are tuned to the vicinity of the
arctic curve arising in the scaling limit, the conjectured determinant
turns into the GUE Tracy–Widom distribution.
Joint work with A. Pronko - ArXiv:2405.04358
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