2 citations · 3 across the 11 of their papers we have counts for
11 papers
Scaling Limit of Critical Loop Soup Clusters in Three, Four, and Five Dimensions
Zhenhao Cai, Jian Ding
We prove that on the metric graph of for , clusters of the critical loop soup (or equivalently, clusters of the critical Gaussian free field level-se…
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…
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'…
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…
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…
Quasi-multiplicativity and regularity for metric graph Gaussian free fields
Zhenhao Cai, Jian Ding
We prove quasi-multiplicativity for critical level-sets of Gaussian free fields (GFF) on the metric graphs (). Specifically, we study the probabi…
One-arm Probabilities for Metric Graph Gaussian Free Fields below and at the Critical Dimension
Zhenhao Cai, Jian Ding
For the critical level-set of the Gaussian free field on the metric graph of , we consider the one-arm probability , i.e., the probability that the boundary of…
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…
A New Correlation Inequality for Ising Models with External Fields
Jian Ding, Jian Song, Rongfeng Sun
We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of b…