Arctic Boundaries of the Ice Model on Three-Bundle Domains

2018/12/10 by Aggarwal, Amol · 3 citations
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.03847

Abstract

In this paper we consider the six-vertex model at ice point on an arbitrary three-bundle domain, which is a generalization of the domain-wall ice model on the square (or, equivalently, of a uniformly random alternating sign matrix). We show that this model exhibits the arctic boundary phenomenon, whose boundary is given by a union of explicit algebraic curves. This was originally predicted by Colomo-Sportiello in 2016 as one of the initial applications of a general heuristic that they introduced for locating arctic boundaries, called the (geometric) tangent method. Our proof uses a probabilistic analysis of non-crossing directed path ensembles to provide a mathematical justification of their tangent method heuristic in this case, which might be of independent interest.

Cited by

• Limit shapes for Domain-Wall (colored) vertex models
• Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
• Frozen-corner enumeration of Alternating Sign Matrices

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