Arctic Boundaries of the Ice Model on Three-Bundle Domains
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, wh...
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| Format: | Report |
| Language: | unknown |
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arXiv
2018
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| Online Access: | https://dx.doi.org/10.48550/arxiv.1812.03847 https://arxiv.org/abs/1812.03847 |
| Summary: | 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. : 45 pages, 15 figures; Version 2: Minor changes in the introduction; Versions 3, 4: Minor changes |
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