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forest
Negative association in uniform forests ★★
Author(s): Pemantle
Conjecture Let
be a finite graph, let
, and let
be the edge set of a forest chosen uniformly at random from all forests of
. Then
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ e,f \in E(G) $](/files/tex/785dc08a907b3bfba9d96f51396e90572dfbc853.png)
![$ F $](/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![\[ {\mathbb P}(e \in F \mid f \in F}) \le {\mathbb P}(e \in F) \]](/files/tex/1fe7ac9c579238670e3aa16ae401e8194e1c3da3.png)
Keywords: forest; negative association
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