Géométrie de la courbe brownienne plane
Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale
On obtient ici le développement asymptotique, en temps petit et sur la diagonale, du noyau de la chaleur associé à un opérateur dégénéré du second ordre satisfaisant à la condition forte d’hypoellipticité de Hörmander.
Grandes déviations de Freidlin-Wentzell en norme höldérienne
Large deviations from the circular law
Singularités des fonctions de Green hypoelliptiques
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...
Internal DLA in a random environment
Hölder norms and the support theorem for diffusions
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.
Poisson convergence for the largest eigenvalues of heavy tailed random matrices
We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in ( (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.
Metastability of the three dimensional Ising model on a torus at very low temperatures.
Elementary potential theory on the hypercube.
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