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

Fingerprint

rectangles
tangents
Rectangle
Tangent line
Defects
Curve
defects
Nonintersecting Lattice Paths
curves
Domino Tilings
Path
Two Parameters
Predict
Configuration
Arbitrary
configurations

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The Arctic Curve for Aztec Rectangles with Defects via the Tangent Method. / Di Francesco, Philippe; Guitter, Emmanuel.

In: Journal of Statistical Physics, Vol. 176, No. 3, 15.08.2019, p. 639-678.

Research output: Contribution to journalArticle

@article{490c88657cb7492dad93a913a36b4048,
title = "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 Schr{\"o}der 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.",
keywords = "Arctic curve, Aztec diamond, Continuum limit, Domino tilings, Non-intersecting lattice paths",
author = "{Di Francesco}, Philippe and Emmanuel Guitter",
year = "2019",
month = "8",
day = "15",
doi = "10.1007/s10955-019-02315-2",
language = "English (US)",
volume = "176",
pages = "639--678",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - The Arctic Curve for Aztec Rectangles with Defects via the Tangent Method

AU - Di Francesco, Philippe

AU - Guitter, Emmanuel

PY - 2019/8/15

Y1 - 2019/8/15

N2 - 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.

AB - 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.

KW - Arctic curve

KW - Aztec diamond

KW - Continuum limit

KW - Domino tilings

KW - Non-intersecting lattice paths

UR - http://www.scopus.com/inward/record.url?scp=85067671340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067671340&partnerID=8YFLogxK

U2 - 10.1007/s10955-019-02315-2

DO - 10.1007/s10955-019-02315-2

M3 - Article

VL - 176

SP - 639

EP - 678

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3

ER -