7 papers · 1 filter
Heterochromatic two-arm probabilities for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
For the Gaussian free field on the metric graph of (), we consider the heterochromatic two-arm probability, i.e., the probability that two points and $v'…
On the gap between cluster dimensions of loop soups on and the metric graph of
Zhenhao Cai, Jian Ding
The question of understanding the scaling limit of metric graph critical loop soup clusters and its relation to loop soups in the continuum appears to be one of the subtle cases th…
Separation and cut edge in macroscopic clusters for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
We prove that for the Gaussian free field (GFF) on the metric graph of (for all except the critical dimension ), with uniformly positive probability…
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…
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…
Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs
Zhenhao Cai, Jian Ding
In this paper, we establish the existence and equivalence of four types of incipient infinite clusters (IICs) for the critical Gaussian free field (GFF) level-set and the critical…