Local Limit of Random Regular Bipartite Planar Maps
Abstract
We prove the existence of the local limit of uniform random d-regular bipartite planar maps, for every d ≥ 3, as the number of vertices tends to infinity. The proof relies on a bijection between maps and so-called blossoming trees established in a previous work. After proving local convergence of the associated decorated trees, we extend the bijection to infinite trees and transfer the convergence to planar maps. The limiting object is almost surely one-ended and recurrent for the simple random walk.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Advanced Combinatorial Mathematics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Preprint