4 papers · 1 filter
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…