Multi-point functions of weighted cubic maps
| Autor: | Jan Ambjørn, Timothy Budd |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
High Energy Physics - Theory Geodesic FOS: Physical sciences 01 natural sciences Interpretation (model theory) 05C80 05C30 60K35 82B41 010104 statistics & probability Planar Theoretical High Energy Physics FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics High Energy Physics 0101 mathematics Scaling Brownian motion Mathematical Physics Mathematics Algebra and Number Theory 010102 general mathematics Mathematical analysis Triangulation (social science) Statistical and Nonlinear Physics First passage percolation Function (mathematics) Mathematical Physics (math-ph) High Energy Physics - Theory (hep-th) ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Geometry and Topology Combinatorics (math.CO) |
| Zdroj: | Annales de l'Institut Henri Poincaré D, 3, 1, pp. 1-44 Annales de l'Institut Henri Poincaré D, 3, 1-44 |
| ISSN: | 2308-5827 |
| DOI: | 10.4171/aihpd/23 |
| Popis: | We study the geodesic two- and three-point functions of random weighted cubic maps, which are obtained by assigning random edge lengths to random cubic planar maps. Explicit expressions are obtained by taking limits of recently established bivariate multi-point functions of general planar maps. We give an alternative interpretation of the two-point function in terms of an Eden model exploration process on a random planar triangulation. Finally, the scaling limits of the multi-point functions are studied, showing in particular that the two- and three-point functions of the Brownian map are recovered as the number of faces is taken to infinity. Comment: 28 pages, 7 figures, several details and clarifications added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|