Institut de recherche mathématique de Rennes

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20022013

most citedCentral limit theorems for eigenvalues in a spiked population model

127 citations

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Showing 2006 · math.PRShow all

8 papers · 2 filters

math.PR2006

Vitesse de Convergence dans le Théorème Limite Central pour Chaînes de Markov de Probabilité de Transition Quasi-Compacte

Loïc Hervé

Let $Q$ be a transition probability on a measurable space $E$ , let $(X_n)_n$ be a Markov chain associated to $Q$ , and let $ξ$ be a real-valued measurable function on $E$ , and $S\…

math.PR2006★ 2 cited

Small noise asymptotic of the timing jitter in soliton transmission

Arnaud Debussche, Eric Gautier

This submission has been withdrawn because it is a duplicate of [math.PR/0609434].

math.PR2006★ 19 cited

Small noise asymptotic of the timing jitter in soliton transmission

Arnaud Debussche, Eric Gautier

We consider the problem of the error in soliton transmission in long-haul optical fibers caused by the spontaneous emission of noise inherent to amplification. We study two types o…

math.PR2006★ 19 cited

Heavy tail properties of stationary solutions of multidimensional stochastic recursions

Yves Guivarc'h

We consider the following recurrence relation with random i.i.d. coefficients $(a_{n}, b_{n})$ : $x_{n + 1} = a_{n + 1} x_{n} + b_{n + 1}$ where $a_{n} \in G L (d, R), b_{n} \in R^{d}$ . Un…

math.PR2006★ 1 cited

Law of Large Numbers for products of random matrices with coefficients in the max-plus semi-ring

Glenn Merlet

We analyze the asymptotic behavior of random variables $x (n, x_0)$ defined by $x (0, x_0) = x_0$ and $x (n + 1, x_0) = A (n) x (n, x_0)$ , where $\sAn$ is a stationary and ergodic sequence of…

math.PR2006

Probabilistic approach for granular media equations in the non uniformly convex case

Patrick Cattiaux, Guillin Arnaud, Malrieu Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the intera…