arXiv subjects

Michael Cantrell

Publications and source records attributed to Michael Cantrell.

2 recordsLinked to original sources

arXiv2016

Differentiability Of Integrable Measurable Cocycles Between Nilpotent Groups

We prove an analog for integrable measurable cocycles of Pansu's differentiation theorem for Lipschitz maps between Carnot-Carathéodory spaces. This yields an alternative, ergodic theoretic proof of Pansu's quasi-isometric rigidity theorem for nilpotent groups, answers a question of Tim Austin regarding integrable measure equivalence between nilpotent groups, and gives an independent proof and strengthening of Austin's result that integrable measure equivalent nilpotent groups have bi-Lipschitz asymptotic cones. Our main tools are a nilpotent-valued cocycle ergodic theorem and a Poincaré recurrence lemma for nilpotent groups.

math.GR↗

arXiv2015

Asymptotic Shapes for Ergodic Families of Metrics on Nilpotent Groups

Let Gamma be a finitely generated nilpotent group. We consider three closely related problems: (i) the asymptotic cone for an equivariant ergodic family of inner metrics on Gamma, generalizing Pansu's theorem; (ii) the limit shapes for First Passage Percolation for general (not necessarily independent) ergodic processes on edges of a Cayley graph of Gamma; (iii) a sub-additive ergodic theorem over a general ergodic Gamma-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 Gamma.

math.GR↗