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Title: Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous works of Benjamini-Tessera and Cantrell-Furman 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 generated virtually nilpotent 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.  more » « less
Award ID(s):
1764421
PAR ID:
10336384
Author(s) / Creator(s):
;
Date Published:
Journal Name:
ArXivorg
ISSN:
2331-8422
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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