Scaling limits of stochastic processes associated with resistance forms
Scaling limits of stochastic processes associated with resistance forms
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DOI：
10.1214/17-aihp861
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发表时间：
2016-09
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影响因子：
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通讯作者：
D. Croydon
中科院分区：
文献类型：
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作者：
D. Croydon
我们确定，如果配备阻力度量和测量的一系列空间相对于格罗莫夫-豪斯多夫模糊拓扑收敛，并且满足一定的非爆炸条件，则相关的随机过程也会收敛。这一结果概括了之前关于树、分形和各种随机图模型的工作。我们进一步推测它将适用于高维整数晶格上临界键渗流的初始无限簇上的随机游走。
We establish that if a sequence of spaces equipped with resistance metrics and measures converge with respect to the Gromov-Hausdorff-vague topology, and a certain non-explosion condition is satisfied, then the associated stochastic processes also converge. This result generalises previous work on trees, fractals, and various models of random graphs. We further conjecture that it will be applicable to the random walk on the incipient infinite cluster of critical bond percolation on the high-dimensional integer lattice.