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Decay of correlations for nonuniformly expanding systems

Sébastien Gouëzel — 2006

Bulletin de la Société Mathématique de France

We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in O ( e - c n ) .

Correlation asymptotics from large deviations in dynamical systems with infinite measure

Sébastien Gouëzel — 2011

Colloquium Mathematicae

We extend a result of Doney [Probab. Theory Related Fields 107 (1997)] on renewal sequences with infinite mean to renewal sequences of operators. As a consequence, we get precise asymptotics for the transfer operator and for correlations in dynamical systems preserving an infinite measure (including intermittent maps with an arbitrarily neutral fixed point).

Random walks on co-compact fuchsian groups

Sébastien GouëzelSteven P. Lalley — 2013

Annales scientifiques de l'École Normale Supérieure

It is proved that the Green’s function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R . It is also shown that Ancona’s inequalities extend to  R , and therefore that the Martin boundary for  R -potentials coincides with the natural geometric boundary S 1 , and that the Martin kernel is uniformly Hölder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, p n ( x , y ) C x , y R - n n - 3 / 2 .

Exponential mixing for the Teichmüller flow

Artur AvilaSébastien GouëzelJean-Christophe Yoccoz — 2006

Publications Mathématiques de l'IHÉS

We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the S L ( 2 , ) action in the moduli space has a spectral gap.

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