| Autor: |
Li, Yiting, Sun, Xin, Watson, Samuel S. |
| Předmět: |
|
| Zdroj: |
Transactions of the American Mathematical Society; Apr2024, Vol. 377 Issue 4, p2439-2493, 55p |
| Abstrakt: |
In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now known as the Schnyder wood , to give a fundamental grid-embedding algorithm for planar maps. In the framework of mating of trees, a uniformly sampled Schnyder-wood-decorated triangulation can produce a triple of random walks. We show that these three walks converge in the scaling limit to three Brownian motions produced in the mating-of-trees framework by Liouville quantum gravity (LQG) with parameter 1, decorated with a triple of SLE_{16}'s curves. These three SLE_{16}'s curves are coupled such that the angle difference between them is 2\pi /3 in imaginary geometry. Our convergence result provides a description of the continuum limit of Schnyder's embedding algorithm via LQG and SLE. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
