Asymptotic shapes for stationary first passage percolation
Asymptotic shapes for stationary first passage percolation
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平稳第一通道渗滤的渐近形状
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
R. Meester
中科院分区：
文献类型：
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作者：
Olle Häggström;R. Meester
本文讨论了第一通道渗流，其中通常的i.i.d.条件被削弱为平稳性（和遍历性）。众所周知的渐近形状的结果是已知的扩展到这种情况下。给出紧集B R d成为关于通过时间的平稳测度的渐近形的必要条件是容易的.我们的主要结果表明，这些条件也是充分的。
This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well known asymptotic shape result is known to extend to this case. It is easy to give necessary conditions for a compact set B ⊂ R d to arise as the asymptotic shape for some stationary measure on the passage times. Our main result says that these conditions are also sufficient.