The Arctic curve for Aztec rectangles with defects via the Tangent Method

The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path configurations are made of Schröder paths whose weights involve t...

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Bibliographic Details
Main Authors: Di Francesco, Philippe, Guitter, Emmanuel
Format: Text
Language:unknown
Published: arXiv 2019
Subjects:
Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Combinatorics math.CO
FOS Physical sciences
FOS Mathematics
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.1902.06478
https://arxiv.org/abs/1902.06478
Description
Summary:The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path configurations are made of Schröder paths whose weights involve two parameters $γ$ and $q$ keeping track respectively of one particular type of step and of the area below the paths. We derive the arctic curve for an arbitrary distribution of defects, and illustrate our result with a number of examples involving different classes of boundary defects. : 46 pages, 18+4 figures

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