Exponential stability for nonlinear filtering
Large deviations from the circular law
Large deviations from the circular law
We prove a full large deviations principle, in the scale N, for the empirical measure of the eigenvalues of an N x N (non self-adjoint) matrix composed of i.i.d. zero mean random variables with variance N. The (good) rate function which governs this rate function possesses as unique minimizer the circular law, providing an alternative proof of convergence to the latter. The techniques are related to recent work by Ben Arous and Guionnet, who treat the self-adjoint case. A crucial role is...
Cut points and diffusive random walks in random environment
Thin points for brownian motion
Einstein relation for biased random walk on Galton–Watson trees
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton–Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrarily slow traps.
Limit theorems for one-dimensional transient random walks in Markov environments
Transportation approach to some concentration inequalities in product spaces.
Consistent minimal displacement of branching random walks.
Maximal arithmetic progressions in random subsets.
Thick points for transient symmetric stable processes.
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