Arctic curves for paths with arbitrary starting points: A tangent method approach

Philippe Di Francesco, Emmanuel Guitter

Research output: Contribution to journalArticle

Abstract

We use the tangent method of Colomo and Sportiello to investigate the arctic curve in a model of non-intersecting lattice paths with arbitrary fixed starting points aligned along some boundary and whose distribution is characterized by some arbitrary piecewise differentiable function. We find that the arctic curve has a simple explicit parametric representation depending of this function, providing us with a simple transform that maps the arbitrary boundary condition to the arctic curve location. We discuss generic starting point distributions as well as particular freezing ones which create additional frozen domains adjacent to the boundary, hence new portions for the arctic curve. A number of examples are presented, corresponding to both generic and freezing distributions. Our results corroborate already known expressions obtained by more involved methods based on bulk correlations, hence providing more evidence to the validity of the tangent method.

Original languageEnglish (US)
Article number355201
JournalJournal of Physics A: Mathematical and Theoretical
Volume51
Issue number35
DOIs
StatePublished - Jul 20 2018

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tangents
Freezing
Tangent line
Path
Curve
Arbitrary
curves
freezing
Nonintersecting Lattice Paths
Boundary conditions
Parametric Representation
Differentiable
Adjacent
Fixed point
Transform
boundary conditions
Model

Keywords

  • arctic curve
  • continuum limit
  • non-intersecting lattice paths

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Arctic curves for paths with arbitrary starting points : A tangent method approach. / Di Francesco, Philippe; Guitter, Emmanuel.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 51, No. 35, 355201, 20.07.2018.

Research output: Contribution to journalArticle

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