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math.PR2026
Negative correlation for the random-cluster model below one on high-degree regular graphs
Pengfei Tang, Zibo Zhang
The random-cluster model with cluster parameter \(0<Q<1\) is conjectured to exhibit negative dependence, but even pairwise negative correlation between distinct edges remains open…
math.PR2026
From second moments to pairwise negative correlation: applications to minimal and uniform spanning trees
Pengfei Tang, Zibo Zhang
We uncover a close connection between the second moment of the degree of a typical vertex in a random subgraph and the pairwise negative correlation (p-NC) property. On one hand, w…
math.PR2026
Pairwise Negative Correlation for Uniform Spanning Subgraphs of the Complete Graph
Pengfei Tang, Zibo Zhang
We investigate the pairwise negative correlation (p-NC) property for uniform probability measures on several families of spanning subgraphs of the complete graph . Motivated b…