Circle packing and Riemann uniformization of random planar maps in an ergodic scale-free environment
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915985604214784 |
|---|---|
| author | Holden, Nina Yu, Pu |
| author_facet | Holden, Nina Yu, Pu |
| contents | We prove that embedded infinite planar maps in ergodic scale-free environments are close to their circle packing and Riemann uniformization embedding on a large scale, as long as suitable moment and connectivity conditions are satisfied. Ergodic scale-free environments were earlier considered by Gwynne, Miller and Sheffield (2018) in the context of the invariance principles for random walk, and they arise naturally in the study of random planar maps and Liouville quantum gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Circle packing and Riemann uniformization of random planar maps in an ergodic scale-free environment Holden, Nina Yu, Pu Probability Complex Variables We prove that embedded infinite planar maps in ergodic scale-free environments are close to their circle packing and Riemann uniformization embedding on a large scale, as long as suitable moment and connectivity conditions are satisfied. Ergodic scale-free environments were earlier considered by Gwynne, Miller and Sheffield (2018) in the context of the invariance principles for random walk, and they arise naturally in the study of random planar maps and Liouville quantum gravity. |
| title | Circle packing and Riemann uniformization of random planar maps in an ergodic scale-free environment |
| topic | Probability Complex Variables |
| url | https://arxiv.org/abs/2603.06528 |