Jian Ding, Zherui Fan, Lu-Jing Huang:Uniqueness of the critical long-range percolation metrics


In this work, we study the random metric for the critical long-range percolation on \mathbb{Z}^d. A recent work by Bäumler [3] 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 [42], and Ding and Gwynne [25] on the uniqueness of Liouville quantum gravity metrics.



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