Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
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几乎幂零群上平稳第一通道渗滤的渐近形状
DOI：
10.1007/s00440-023-01196-7
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发表时间：
2023
影响因子：
2
通讯作者：
Gorski, Christian
中科院分区：
文献类型：
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作者：
Auffinger, Antonio;Gorski, Christian
本文研究了一类具有固定边权的Cayley图的首次通过渗流问题。Benjamini和Tessera（Electron J Probab 20：1-20，2015）以及Cantrell和Furman（Groups Geom Dyn 11（4）：1307-1345，2017）的先前工作表明，此类FPP的标度极限由相关分次幂零李群上的Carnot-Carathéodory度量给出。我们证明了一个匡威的结果，即对于一个分次生成的幂零群的任何Cayley图，其分次幂零李群上的任何Carnot-Carathéodory度量都是该图上具有固定边权的FPP的标度极限.此外，对于任意非共轭生成的虚幂零群的Cayley图，任何“共轭不变”度量都是该图上具有固定边权的FPP的标度极限。我们还表明，“共轭不变”的条件也是一个必要条件，在所有情况下，标度限制已知存在。
We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous works of Benjamini and Tessera (Electron J Probab 20:1–20, 2015) and Cantrell and Furman (Groups Geom Dyn 11(4):1307–1345, 2017) show that scaling limits of such FPP are given by Carnot-Carathéodory metrics on the associated graded nilpotent Lie group. We show a converse, i.e. that for any Cayley graph of a finitely generated nilpotent group, any Carnot-Carathéodory metric on the associated graded nilpotent Lie group is the scaling limit of some FPP with stationary edge weights on that graph. Moreover, for any Cayley graph of any finitely generatedvirtuallynilpotent group, any “conjugation-invariant” metric is the scaling limit of some FPP with stationary edge weights on that graph. We also show that the “conjugation-invariant” condition is also a necessary condition in all cases where scaling limits are known to exist.
DOI：
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发表时间：
1995
期刊：
影响因子：
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作者：
Olle Häggström;R. Meester
通讯作者：
R. Meester