Pna Probability, Networks and Algorithms Probability, Networks and Algorithms Self-destructive Percolation Self-destructive Percolation
Pna Probability, Networks and Algorithms Probability, Networks and Algorithms Self-destructive Percolation Self-destructive Percolation
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Pna 概率、网络和算法 概率、网络和算法 自毁渗透 自毁渗透
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通讯作者：
R. Brouwer
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作者：
J. Van Den Berg;R. Brouwer
CWI的研究具有主题导向的结构，并分为四个集群。下面列出的是集群的名称，括号内是它们的缩写。考虑一个无限图上的普通点渗透，其中的点彼此独立，被占用的概率为p，空的概率为1−p。现在假设，由于某种“灾难”，在一个无限被占用的簇中的所有位置都空了。最后，每个空置的站点都得到了额外的增强，从而被占用。更准确地说，每一个已经空置或因灾难而空置的位置，都以δ概率（与其他位置无关）被占用。当p大于但接近临界值p c时，人们可能会认为（对于“漂亮”的图），在最终构型中，只需要一个小的δ就可以拥有一个无限占用的簇。二叉树的情况似乎确实如此。然而，在方形晶格上，我们强烈推测这是不正确的。我们讨论了这些问题的背景，并表明，这个猜想，如果成立，有一些显著的后果。注：本报告已提交给其他地方出版。这项工作是在项目PNA 3.1下进行的。
CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ABSTRACT Consider ordinary site percolation on an infinite graph in which the sites, independent of each other, are occupied with probability p and vacant with probability 1−p. Now suppose that, by some 'catastrophe', all sites which are in an infinite occupied cluster become vacant. Finally, each vacant site gets an extra enhancement to become occupied. More precisely, each site that was already vacant or that was made vacant by the catastrophe, becomes occupied with probability δ (independent of the other sites). When p is larger than but close to the critical value p c one might believe (for 'nice' graphs) that only a small δ is needed to have an infinite occupied cluster in the final configuration. This appears to be indeed the case for the binary tree. However, on the square lattice we strongly conjecture that this is not true. We discuss the background for these problems and also show that the conjecture, if true, has some remarkable consequences. Note: This report has been submitted for publication elsewere. This work has been done under project PNA 3.1.