[Papers]
[Alex Furman]

Asymptotic shapes for ergodic families of metrics on nilpotent groups

Let G be a finitely generated, virtually nilpotent group. We consider three closely related problems:

(i) description of the asymptotic cone for an equivariant ergodic family of inner metrics on G, generalizing Pansu's theorem;

(ii) existence of the limit shapes for First Passage Percolation for general (not necessarily independent) ergodic process on edges of a Cayley graph of G;

(iii) formulation of a sub-additive ergodic theorem over a general ergodic G-action.

The limiting objects are given in terms of a Carnot-Caratheodory metric on the graded nilpotent group associated to the Mal'cev completion of G.

Authors:
M. Cantrell, A. Furman

Bibliographical:
Groups, Geom., Dynam., Groups Geom. Dyn. **11** (2017), no. 4, 1307–1345

Download: pdf | published |
arXiv:1508.00244

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[Papers]
[Alex Furman]