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

Abstract

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 $\gamma$ 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.

arXiv comment46 pages, 18+4 figures

References in corpus (8)

• The Refined Topological Vertex
• The arctic curve of the domain-wall six-vertex model
• Arctic curves of the six-vertex model on generic domains: the Tangent Method
• The limit shape of large alternating sign matrices
• Arctic curve of the free-fermion six-vertex model in an L-shaped domain
• A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points
• Arctic curves for paths with arbitrary starting points: a tangent method approach
• Arctic Curves in path models from the Tangent Method

Cited by in corpus (6)

• Arctic curves of the twenty-vertex model with domain wall boundaries
• Arctic curves of the four-vertex model
• Arctic curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex models
• Arctic curves of the 20V model on a triangle
• Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition