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

Article number | 115205 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 52 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 2019 |

### 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

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 52, no. 11, 115205. https://doi.org/10.1088/1751-8121/ab03ff

}

TY - JOUR

T1 - A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points

AU - Di Francesco, Philippe

AU - Guitter, Emmanuel

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - arctic curve

KW - continuum limit

KW - non-intersecting lattice paths

UR - http://www.scopus.com/inward/record.url?scp=85063473257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063473257&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ab03ff

DO - 10.1088/1751-8121/ab03ff

M3 - Article

VL - 52

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 11

M1 - 115205

ER -