47 citations · 51 across the 7 of their papers we have counts for
12 papers
Random free semigroups of affine groups
Richard Aoun, Keivan Mallahi-Karai
We investigate random freeness of semigroups in the solvable non-virtually nilpotent setting. We focus on a correlated affine model, namely semigroups generated by the two componen…
Recurrence of multidimensional affine recursions in the critical case
Richard Aoun, Sara Brofferio, Marc Peigné
We prove, under different natural hypotheses, that the random multidimensional affine recursion , is recurrent in the critical case. In…
Stationary probability measures on projective spaces 2: the critical case
Richard Aoun, Cagri Sert
In a previous article, given a finite-dimensional real vector space and a probability measure on with finite first moment, we gave a description of…
Stationary probability measures on projective spaces for block-Lyapunov dominated systems
Richard Aoun, Cagri Sert
Given a finite-dimensional real vector space , a probability measure on and a -invariant subspace , under a block-Lyapunov contraction assumpti…
Random walks on hyperbolic spaces: second order expansion of the rate function at the drift
Richard Aoun, Pierre Mathieu, Cagri Sert
Let be a geodesic Gromov-hyperbolic space, a basepoint and a countably supported non-elementary probability measure on . Denote by $z_…
Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternative
Richard Aoun, Cagri Sert
The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks…
Matrix Poincaré inequalities and concentration
Richard Aoun, Marwa Banna, Pierre Youssef
We show that any probability measure satisfying a Matrix Poincaré inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequali…
Law of large numbers for the spectral radius of random matrix products
Richard Aoun, Cagri Sert
We prove that the spectral radius of an i.i.d.\ random walk on $\GL_d(\C)$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large num…
The central limit theorem for eigenvalues
Richard Aoun
We prove that the spectral radius of a strongly irreducible random walk on GLd(R) (or more generally the vector of moduli of eigenvalues of a Zariski-dense random walk on a reducti…
Random matrix products when the top Lyapunov exponent is simple
Richard Aoun, Yves Guivarc'h
In the present paper, we treat random matrix products on the general linear group , where is a vector space defined on any local field, when the top Lyapunov ex…
Transience of algebraic varieties in linear groups and application to generic Zariski density
Richard Aoun
We study the transience of algebraic varieties in linear groups. In particular, we show that a "non elementary" random walk in SL_2(R) escapes exponentially fast from every proper…
Random subgroups of linear groups are free
Richard Aoun
We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will h…