Uniqueness of the Critical Long-Range Percolation Metrics
Abstract
In this work, we study the random metric for the critical long-range percolation on Z d \mathbb {Z}^d . A recent work by Bäumler (2022) implies the subsequential scaling limit, and our main contribution is to prove that the subsequential limit is uniquely characterized by a natural list of axioms. Our proof method is hugely inspired by recent works of Gwynne and Miller (2021b), and Ding and Gwynne (2023a) on the uniqueness of Liouville quantum gravity metrics.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Random Matrices and Applications
Geometry and complex manifolds
Publication details
- Journal / source
- Memoirs of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 318
- Issue
- 1620
- Publication date
- 27 February 2026
- Language
- EN