First passage percolation on nilpotent Cayley graphs and beyond

Understand

Our main result is an extension of Pansu's theorem to random metrics, where the edges of the Cayley are i.i.d.

• random variable with some finite exponential moment.
• Based on a previous work by the second author, the proof relies on Talagrand's concentration inequality, and on Pansu's theorem.
• Adapting a well-known argument for Z^d, we prove a sublinear estimate on the variance for virtually nilpotent groups which are not virtually isomorphic to Z.