Poisson boundaries of building lattices and rigidity with hyperbolic-like targets
Group Theory
2025-05-07 v1 Geometric Topology
Probability
Abstract
We prove that a Poisson boundary of any regular thick Euclidean building, as well as lattices thereof is the space of chambers at infinity of the building with the harmonic measure class. We then use this result to generalize rigidity results of Guirardel-Horbez-L\'ecureux on morphisms and cocycles from lattices in buildings to groups with negative curvature properties.
Keywords
Cite
@article{arxiv.2505.02855,
title = {Poisson boundaries of building lattices and rigidity with hyperbolic-like targets},
author = {Antoine Derimay},
journal= {arXiv preprint arXiv:2505.02855},
year = {2025}
}
Comments
48 pages. Comments welcome! arXiv admin note: text overlap with arXiv:2005.07477 by other authors