1 citations · 1 across the 5 of their papers we have counts for
6 papers
Uniqueness and dimension for the geodesic of the critical long-range percolation metric
Jian Ding, Zherui Fan, Lu-Jing Huang
By recent works of Bäumler [2] and of the authors of this paper [5], the (limiting) random metric for the critical long-range percolation was constructed. In this paper, we prove t…
Spectral dimensions for one-dimensional critical long-range percolation
Zherui Fan, Lu-Jing Huang
Consider the critical long-range percolation on , where an edge connects and independently with probability $1-\exp\{-β\int_i^{i+1}\int_j^{j+1}|u-v|^{-2}d ud v\…
The polynomial growth of effective resistances in one-dimensional critical long-range percolation
Jian Ding, Zherui Fan, Lu-Jing Huang
We study the critical long-range percolation on , where an edge connects and independently with probability $1-\exp\{-β\int_i^{i+1}\int_j^{j+1}|u-v|^{-2}{\rm d}…
Polynomial lower bound on the effective resistance for the one-dimensional critical long-range percolation
Jian Ding, Zherui Fan, Lu-Jing Huang
In this work, we study the critical long-range percolation on , where an edge connects and independently with probability for some fixe…
Uniqueness of the critical long-range percolation metrics
Jian Ding, Zherui Fan, Lu-Jing Huang
In this work, we study the random metric for the critical long-range percolation on . A recent work by Bäumler [3] implies the subsequential scaling limit, and our ma…
Roughness of geodesics in Liouville quantum gravity
Zherui Fan, Subhajit Goswami
The metric associated with the Liouville quantum gravity (LQG) surface has been constructed through a series of recent works and several properties of its associated geodesics have…