Arctic Curves for Ice Models

Explore the fascinating world of arctic curves in ice models through this 51-minute lecture from the Asymptotic Algebraic Combinatorics 2020 conference. Delve into the existence and determination of arctic boundaries in two-dimensional statistical mechanics models, focusing on the six-vertex model with domain-wall boundary conditions. Learn about the probabilistic analysis of non-crossing directed path ensembles and gain insights into the mathematical justification of the geometric tangent method. Discover the interplay between alternating sign matrices, frozen regions, and boundary parameterization in ice models. Examine the trajectory of the bottom path, tangency assumptions, and the process of determining arctic boundaries. Gain a deeper understanding of the tangent method heuristic, notation conventions, and boundary data analysis. Explore concepts such as monotone couplings and linearity estimates, essential for comprehending the intricate proof methodologies in this field of study.

Intro
Alternating Sign Matrices
Frozen Region of an ASM
Boundary Parameterization
Six-Vertex Ensembles and Ice Models
Trajectory of the Bottom Path of the Ice Model
Tangency Assumption
Determining the Arctic Boundary
Tangent Method Heuristic
Notation
Boundary Data
Monotone Couplings
Linearity Estimates
Proof of