Nucleation scaling in jigsaw percolation
Nucleation scaling in jigsaw percolation
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拼图渗流中的成核缩放
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
David J Sivakoff
中科院分区：
文献类型：
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作者：
Janko Gravner;David J Sivakoff
拼图渗透是一种非局部过程，它“通过使用随机人物图的连接属性”在同一组顶点上迭代地合并确定性拼图图中的连接簇。我们假设 Erd} os-R enyi 人图的边概率为 p，并研究谜题被解决的概率，即该过程最终产生单个簇的概率。一般来说，对于具有 N 个关于 D 度数的顶点的拼图图（在适当的意义上），该概率接近 1 或很小，具体取决于 pD logN 是大还是小。对一维环和二维环面谜题进行了更详细的研究，并且在许多情况下获得了临界概率的精确缩放。主要工具来自自举渗透和其他局部成核与生长模型的分析。该论文解决了 Brummitt、Chatterjee、Dey 和 Sivako 提出的几个猜想，他们认为
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic puzzle graph" by using connectivity properties of a random people graph" on the same set of vertices. We presume the Erd} os-R enyi people graph with edge probability p and investigate the probability that the puzzle is solved, that is, that the process eventually produces a single cluster. In some generality, for puzzle graphs with N vertices of degrees about D (in the appropriate sense), this probability is close to 1 or small depending on whether pD logN is large or small. The one dimensional ring and two dimensional torus puzzles are studied in more detail and in many cases the exact scaling of the critical probability is obtained. Main tools come from analysis of bootstrap percolation and other local nucleation-and-growth models. The paper settles several conjectures posed by Brummitt, Chatterjee, Dey, and Sivako who