Using the tangent method to compute arctic curves

by Bryan Debin (UCLouvain)

Location: 200B.02.18, Leuven
Time: Thursday November 29, 2018 at 14:00

The study of the arctic phenomenon is often performed by evaluating “bulk” observables. We present another approach, called the tangent method, due to Colomo and Sportiello. We illustrate this method in a particular random tiling problem, defined in the scaling limit by an arbitrary piecewise continuous function. A single arctic curve is observed for a generic choice of this function, but other additional pieces of arctic curve appear when this function has specific features. We explicitly compute the parametric equation of one of these using the tangent method, and sketch the computation for all other portions.