Filippo Colomo - Frozen boundaries and their fluctuations in the square-ice model - IPAM at UCLA

Recorded 20 May 2024. Filippo Colomo of INFN - Sezione di Firenze presents "Frozen boundaries and their fluctuations in the square-ice model" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop.
Abstract: 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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