Scaling limit of random plane quadrangulations with a simple boundary, via restriction
| Autor: | Bettinelli, Jérémie, Curien, Nicolas, Fredes, Luis, Sepúlveda, Avelio |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence $(p_n)$ of even positive integers with $p_n\sim 2\alpha \sqrt{2n}$ for some $\alpha\in(0,\infty)$. Then, for the Gromov--Hausdorff topology, a quadrangulation with a simple boundary uniformly sampled among those with $n$ inner faces and boundary length $p_n$ weakly converges, in the usual scaling $n^{-1/4}$, toward the Brownian disk of perimeter $3\alpha$. Our method consists in seeing a uniform quadrangulation with a simple boundary as a conditioned version of a model of maps for which the Gromov--Hausdorff scaling limit is known. We then explain how classical techniques of unconditionning can be used in this setting of random maps. Comment: This is the updated version of the paper previously entitled "Nonbijective scaling limit of maps via restriction." |
| Databáze: | arXiv |
| Externí odkaz: |
|