Geodesic
Asymptotic shapes for ergodic families of metrics on Nilpotent groups
Michael Cantrell1 ; Alex Furman1
1University of Illinois at Chicago, USA
Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1307-1345

Voir la notice de l'article provenant de la source EMS Press

DOI

Let Γ be a finitely generated virtually nilpotent group. We consider three closely related problems: (i) convergence to a deterministic asymptotic cone for an equivariant ergodic family of inner metrics on Γ, generalizing Pansu's theorem; (ii) the asymptotic shape theorem for first passage percolation for general (not necessarily independent) ergodic processes on edges of a Cayley graph of Γ; (iii) the sub-additive ergodic theorem over a general ergodic Γ-action. The limiting objects are given in terms of a Carnot–Carathéodory metric on the graded nilpotent group associated to the Mal'cev completion of Γ.
DOI : 10.4171/ggd/430
Classification : 37-XX, 53-XX
Mots-clés : Subadditive ergodic theorem, Carnot group, first passage percolation

Michael Cantrell  1   ; Alex Furman  1

1 University of Illinois at Chicago, USA 
Michael Cantrell; Alex Furman. Asymptotic shapes for ergodic families of metrics on Nilpotent groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1307-1345. doi: 10.4171/ggd/430
@article{10_4171_ggd_430,
     author = {Michael Cantrell and Alex Furman},
     title = {Asymptotic shapes for ergodic families of metrics on {Nilpotent} groups},
     journal = {Groups, geometry, and dynamics},
     pages = {1307--1345},
     year = {2017},
     volume = {11},
     number = {4},
     doi = {10.4171/ggd/430},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/430/}
}
TY  - JOUR
AU  - Michael Cantrell
AU  - Alex Furman
TI  - Asymptotic shapes for ergodic families of metrics on Nilpotent groups
JO  - Groups, geometry, and dynamics
PY  - 2017
SP  - 1307
EP  - 1345
VL  - 11
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/430/
DO  - 10.4171/ggd/430
ID  - 10_4171_ggd_430
ER  - 
%0 Journal Article
%A Michael Cantrell
%A Alex Furman
%T Asymptotic shapes for ergodic families of metrics on Nilpotent groups
%J Groups, geometry, and dynamics
%D 2017
%P 1307-1345
%V 11
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/430/
%R 10.4171/ggd/430
%F 10_4171_ggd_430

Cité par Sources :