Speaker: Alan Hammond
ABSTRACT: When a low-temperature Ising model in a box with negative
boundary conditions is conditioned on the presence of a significant
excess of plus signs, this excess tends to gather together in a droplet
of the plus phase, surrounded by a sea of the minus phase. Between the
droplet and its surroundings is a dual contour, the droplet boundary.
I will discuss the fluctuation of such boundaries from their convex
hull, introducing local notions of deviation, and explain how the
longitudinal and lateral deviations in the droplet boundary have
exponents coinciding with those in the KPZ class of growing
interfaces. A key tool in the proofs are resampling and surgical
techniques tha are also useful studying random objects in the KPZ
class, such as the multi-line Airy process.