A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points

Philippe Di Francesco, Emmanuel Guitter

Research output: Contribution to journalArticle

Abstract

We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a q-dependent weight associated with the area delimited by the paths. Our model is characterized by an arbitrary sequence of starting points along the positive horizontal axis, whose distribution involves an arbitrary piecewise differentiable function. We give an explicit expression for the arctic curve in terms of this arbitrary function and of the parameter q. A particular emphasis is put on the deformation of the arctic curve upon varying q, and on its limiting shapes when q tends to 0 or infinity. Our analytic results are illustrated by a number of detailed examples.

Original languageEnglish (US)
Article number115205
JournalJournal of Physics A: Mathematical and Theoretical
Volume52
Issue number11
DOIs
StatePublished - Jan 1 2019

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tangents
Tangent line
derivation
Path
Curve
Arbitrary
Nonintersecting Lattice Paths
curves
Quadrant
quadrants
infinity
Differentiable
Horizontal
Limiting
Infinity
Tend
Dependent
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

A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points. / Di Francesco, Philippe; Guitter, Emmanuel.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 11, 115205, 01.01.2019.

Research output: Contribution to journalArticle

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