Eigenvalue curves of asymmetric tridiagonal random matrices.
Ergodicity for the stochastic complex Ginzburg–Landau equations
Ergodicity of increments of the Rosenblatt process and some consequences
A new proof of the mixing property of the increments of Rosenblatt processes is given. The proof relies on infinite divisibility of the Rosenblatt law that allows to prove only the pointwise convergence of characteristic functions. Subsequently, the result is used to prove weak consistency of an estimator for the self-similarity parameter of a Rosenblatt process, and to prove the existence of a random attractor for a random dynamical system induced by a stochastic reaction-diffusion equation driven...
Ergodicity of PCA: equivalence between spatial and temporal mixing conditions.
Estimates for Principal Lyapunov Exponents: A Survey
This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....
Existence of non-uniform cocycles on uniquely ergodic systems
Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems
We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space for finite , partially answering...
Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée
On montre que les exposants de Lyapunov de l’algorithme de Jacobi-Perron, en dimension quelconque, sont tous différents et que la somme des exposants extrêmes est strictement positive. En particulier, si , le deuxième exposant est strictement négatif.