### 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 language | English (US) |
---|---|

Article number | 355201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 51 |

Issue number | 35 |

DOIs | |

State | Published - Jul 20 2018 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 51, no. 35, 355201. https://doi.org/10.1088/1751-8121/aad028

}

TY - JOUR

T1 - Arctic curves for paths with arbitrary starting points

T2 - A tangent method approach

AU - Di Francesco, Philippe

AU - Guitter, Emmanuel

PY - 2018/7/20

Y1 - 2018/7/20

N2 - 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.

AB - 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.

KW - arctic curve

KW - continuum limit

KW - non-intersecting lattice paths

UR - http://www.scopus.com/inward/record.url?scp=85050736015&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050736015&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aad028

DO - 10.1088/1751-8121/aad028

M3 - Article

AN - SCOPUS:85050736015

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 35

M1 - 355201

ER -