Nondistorsion des horosphères dans des immeubles euclidiens et dans des espaces symétriques

We give a necessary and sufficient condition for a horosphere to be undistorted in an Euclidean building and in a symmetric space. We are using the geometry of Euclidean buildings and the asymptotic cone. As a consequence, a geometric proof of the Lubotzky-Mozes-Raghunathan theorem for ℚ-rank one la...