INVARIANT MONOTONE COUPLING NEED NOT EXIST

• 成果类型: Article
• 署名作者: Mester, Peter
• 署名单位: Indiana University System; Indiana University Bloomington
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP767
• 发表日期: 2013
• 页码: 1180-1190
• 关键词: uniform spanning forests

摘要

We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that X subset of Y, although no such coupling can be invariant. Here, invariant means that the distribution is invariant under group multiplications.