A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points
| Autor: | Philippe Di Francesco, Emmanuel Guitter |
|---|---|
| Přispěvatelé: | Department of Mathematics, Illinois State University, Illinois State University, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay, ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
non-intersecting lattice paths FOS: Physical sciences General Physics and Astronomy 01 natural sciences Quadrant (plane geometry) 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics arctic curve Differentiable function continuum limit 0101 mathematics 010306 general physics Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics Horizontal axis [PHYS]Physics [physics] Statistical Mechanics (cond-mat.stat-mech) 010102 general mathematics Mathematical analysis Tangent Statistical and Nonlinear Physics Mathematical Physics (math-ph) Limiting Arbitrary function The arctic Modeling and Simulation Piecewise Combinatorics (math.CO) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical Journal of Physics A: Mathematical and Theoretical, 2019, 52 (11), pp.115205. ⟨10.1088/1751-8121/ab03ff⟩ Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2019, 52 (11), pp.115205. ⟨10.1088/1751-8121/ab03ff⟩ |
| ISSN: | 1751-8113 1751-8121 |
| DOI: | 10.1088/1751-8121/ab03ff⟩ |
| Popis: | 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. 48 pages, 21 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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