The Arctic Curve for Aztec Rectangles with Defects via the Tangent Method

Philippe Di Francesco, Emmanuel Guitter

Research output: Contribution to journalArticle

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 γ and q keeping track respectively of one particular type of step and of the area below the paths. We predict the arctic curve for an arbitrary distribution of defects, and illustrate our result with a number of examples involving different classes of boundary defects.

Original languageEnglish (US)
Pages (from-to)639-678
Number of pages40
JournalJournal of Statistical Physics
Volume176
Issue number3
DOIs
StatePublished - Aug 15 2019

Keywords

  • Arctic curve
  • Aztec diamond
  • Continuum limit
  • Domino tilings
  • Non-intersecting lattice paths

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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