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pro vyhledávání: '"Aoun, Richard"'
We prove, under different natural hypotheses, that the random multidimensional affine recursion $X_n=A_nX_{n-1}+B_n\in\mathbb{R}^d, n \geq 1,$ is recurrent in the critical case. In particular we cover the cases where the matrices $A_n$ are similariti
Externí odkaz:
http://arxiv.org/abs/2408.03853
Autor:
Aoun, Richard, Sert, Cagri
In a previous article, given a finite-dimensional real vector space $V$ and a probability measure $\mu$ on $\operatorname{PGL}(V)$ with finite first moment, we gave a description of all $\mu$-stationary probability measures on the projective space $\
Externí odkaz:
http://arxiv.org/abs/2305.02879
Autor:
Aoun, Richard, Sert, Cagri
Given a finite-dimensional real vector space $V$, a probability measure $\mu$ on $\operatorname{PGL}(V)$ and a $\mu$-invariant subspace $W$, under a block-Lyapunov contraction assumption, we prove existence and uniqueness of lifts to $P(V)\setminus P
Externí odkaz:
http://arxiv.org/abs/2202.08014
Let $(X,d)$ be a geodesic Gromov-hyperbolic space, $o \in X$ a basepoint and $\mu$ a countably supported non-elementary probability measure on $\operatorname{Isom}(X)$. Denote by $z_n$ the random walk on $X$ driven by the probability measure $\mu$. S
Externí odkaz:
http://arxiv.org/abs/2112.14724
Autor:
Aoun, Richard, Sert, Cagri
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 on hyperbolic spaces. For a proper hyperbolic space $M$, we obtain ex
Externí odkaz:
http://arxiv.org/abs/2101.08222
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ operator. Thi
Externí odkaz:
http://arxiv.org/abs/1910.13797
Autor:
Aoun, Richard, Sert, Cagri
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 numbers under finite first moment. No irreducibility assumption is suppos
Externí odkaz:
http://arxiv.org/abs/1908.07469
Autor:
Aoun, Richard
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 reductive group) satisfies a central limit theorem under an order two moment
Externí odkaz:
http://arxiv.org/abs/1902.09202
Autor:
Aoun, Richard
Publikováno v:
Enseign. Math., 43, 171-198, 2013
Let $G$ be a real linear semisimple algebraic group without compact factors and $\Gamma$ a Zariski dense subgroup of $G$. In this paper, we use a probabilistic counting in order to study the asymptotic properties of $\Gamma$ acting on the Furstenberg
Externí odkaz:
http://arxiv.org/abs/1707.02186
Autor:
Aoun, Richard, Guivarc'h, Yves
Publikováno v:
J. Eur. Math. Soc. (JEMS) 22 (2020), no. 7, 2135-2182
In the present paper, we treat random matrix products on the general linear group $\textrm{GL}(V)$, where $V$ is a vector space defined on any local field, when the top Lyapunov exponent is simple, without irreducibility assumption. In particular, we
Externí odkaz:
http://arxiv.org/abs/1705.09593