Spectral gap properties and limit theorems for some random walks and dynamical systems

Yves Guivarc'H (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We give a description of some limit theorems and the corresponding proofs for various transfer operators. Our examples are closely related with random walks on homogeneous spaces. The results are obtained using spectral gap methods in Hölder spaces or Hilbert spaces. We describe also their geometrical setting and the basic corresponding properties. In particular we focus on precise large deviations for products of random matrices, Fréchet's law for affine random walks and local limit theorems for Euclidean motion groups or nilmanifolds.

Domaines: Probabilités [math.PR]

Yves Guivarc'H. Spectral gap properties and limit theorems for some random walks and dynamical systems. D. Dolgopyat, Y. Pesin, M. Pollicott and L. Stoyanov. Hyperbolic Dynamics, Fluctuations and Large Deviations, 89, American Mathematical Society, pp.279-310, 2015, Proceedings of Symposia in Pure Mathematics, 978-1-4704-1112-1. ⟨hal-01022414⟩