Arctic curves for paths with arbitrary starting points: a tangent method approach - Archive ouverte HAL Access content directly
Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2018

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

(1, 2) , (1)
1
2

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.
Fichier principal
Vignette du fichier
gUITT.pdf (1.85 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

cea-02011867 , version 1 (08-02-2019)

Identifiers

Cite

Philippe Di Francesco, Emmanuel Guitter. Arctic curves for paths with arbitrary starting points: a tangent method approach. Journal of Physics A: Mathematical and Theoretical, 2018, 51, pp.355201. ⟨10.1088/1751-8121/aad028⟩. ⟨cea-02011867⟩
57 View
76 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More