有限连通图上随机扩张森林和连通子图的边负相关性

Edge-Negative Association in Random Spanning Forests and Connected Subgraphs on Connected Finite Graphs

设G为有限连通图．本文研究图G的子图空间G上的三类概率测度,它们分别刻画图的随机扩张树,随机扩张森林和随机连通子图．基于G上均匀扩张树的边负相关性,我们构造G上的一族边负相关的非平凡随机扩张森林和随机连通子图．此外,我们还给出一定条件下图上均匀扩张森林的边负相关性．

Let G be a connected finite graph. Wc consider three types of probability measures on G, the set of subgraphs of G, which govern a random spanning tree, a random spanning forest, and a random connected subgraph respectively. Basing on the edge-negative association in uniform spanning tree , we construct a family of random spanning forests and random connected subgraphs on G which are edge-negative associated. Finally, we prove the edge-negative association property for uniform spanning forest in a special case of G.