Scaling limit of triangulations of polygons
| Autor: | Xin Sun, Marie Albenque, Nina Holden |
|---|---|
| Přispěvatelé: | Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Brownian disk 05C80 Boundary (topology) triangulation Type (model theory) Computer Science::Computational Geometry 01 natural sciences Combinatorics 010104 statistics & probability Simple (abstract algebra) Gromov-Hausdorff-Prokhorov-uniform topology Mathematics::Category Theory [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] FOS: Mathematics Mathematics - Combinatorics scaling limit 0101 mathematics 60D05 Brownian motion ComputingMilieux_MISCELLANEOUS Mathematics 010102 general mathematics Probability (math.PR) Triangulation (social science) Triangulation Scaling limit 60F17 Bijection Embedding Combinatorics (math.CO) Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Electronic Journal of Probability Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2020, 25, ⟨10.1214/20-EJP537⟩ Electronic Journal of Probability, 25 Electron. J. Probab. |
| ISSN: | 1083-6489 |
| DOI: | 10.1214/20-EJP537⟩ |
| Popis: | We prove that random triangulations of types I, II, and III with a simple boundary under the critical Boltzmann weight converge in the scaling limit to the Brownian disk. The proof uses a bijection due to Poulalhon and Schaeffer between type III triangulations of the p-gon and so-called blossoming forests. A variant of this bijection was also used by Addario-Berry and the first author to prove convergence of type III triangulations to the Brownian map, but new ideas are needed to handle the simple boundary. Our result is an ingredient in the program of the second and third authors on the convergence of uniform triangulations under the Cardy embedding. Electronic Journal of Probability, 25 ISSN:1083-6489 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|