A general fixed point theorem for isometries in terms of metric functionals is proved under
the assumption of the existence of a conical bicombing. It is new for isometries of convex …

We show under weak hypotheses that the pushforward fZnog of a random-walk to a CAT (0)
cube complex converges to a point on the boundary. We introduce the notion of squeezing …

We initiate the study of random iteration of automorphisms of real and complex projective
surfaces, as well as compact Kähler surfaces, focusing on the classification of stationary …

We consider dynamical and geometrical aspects of deep learning. For many standard
choices of layer maps we display semi-invariant metrics which quantify differences between …

This article presents the beginning of a metric functional analysis. A major notion is metric
functionals which extends that of horofunctions in metric geometry. Applications of the main …

The Oseledets multiplicative ergodic theorem is a basic result with numerous applications
throughout dynamical systems. These notes provide an introduction to this theorem, as well …

Consider (gn) n≥ 1 a sequence of independent and identically distributed random matrices
and the left random walk G n:= gn… g 1, n≥ 1 on the general linear group GL (d, R). Under …

This paper discusses a general method for spectral type theorems using metric spaces
instead of vector spaces. Advantages of this approach are that it applies to genuinely non …

The notion of metric compactification was introduced by Gromov and later rediscovered by
Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a …

Let $(g_n) _ {n\geq 1} $ be a sequence of independent and identically distributed random
elements with law $\mu $ on the general linear group $\textrm {GL}(V) $, where $ V=\mathbb …