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arXiv · 2308.00621

Uniqueness of the critical long-range percolation metrics

Jian Ding·Zherui Fan·Lu-Jing Huang
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Abstract

In this work, we study the random metric for the critical long-range percolation on $\mathbb{Z}^d$. A recent work by B\"aumler [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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Jian Ding, Zherui Fan, Lu-Jing Huang. 2023-08-01. Uniqueness of the critical long-range percolation metrics. https://arxiv.org/abs/2308.00621

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