MIT Probability Seminar
Monday, March 09, 2020 at 4:15pm to 5:15pm
182 MEMORIAL DR, Cambridge, MA 02139
Title : The five-vertex model
The five vertex model is a probability measure on monotone nonintersecting lattice paths, where each corner of each path gets weight r. It generalizes the lozenge tiling model which is the case r=1. There is a rigorous "Bethe Ansatz" solution, leading to explicit limit shapes for tilings of bounded regions such as the boxed plane partition.
Fluctuations around the limit shape are conjecturally given by a Gaussian free field with a spatially-varying stiffness. We discuss a recent approach to getting local statistics in the model.