[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) the asymptotic cone for an equivariant ergodic family of inner metrics on G, generalizing Pansu's theorem;
(ii) the limit shapes for First Passage Percolation for general (not necessarily independent) ergodic process on edges of a Cayley graph of G;
(iii) 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: preprint, pp. 28
Download: pdfarXiv:1508.00244



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[Papers] [Alex Furman]