Directeur de recherche CNRS de deuxième classe

Laboratoire Jean Leray

2 rue de la Houssinière - BP92208

44322 NANTES CEDEX 3

France

**E-mail :** sebastien.gouezel "at" univ-nantes.fr

**Bureau :** 137

**Téléphone :** 02 76 64 50 05

C.V.

### Research articles:

### Other documents:

### Proof assistants:

Out of curiosity, I have given a try to several proof assistants, i.e., computer programs on which one can formalize
and check mathematical proofs, from the most basic statements (definition of real numbers, say) to
the most advanced ones (hopefully including current research in a near or distant future).
The only one I have managed to use efficiently is Isabelle/HOL,
which is (from my point of view) by far the most convenient for mathematicians. In addition to several
facts that have been added to the main library (for instance conditional expectations), I have developed the
following theories:

Laboratoire Jean Leray

2 rue de la Houssinière - BP92208

44322 NANTES CEDEX 3

France

C.V.

39. | Quantitative Pesin theory for Anosov diffeomorphisms and flows (with L. Stoyanov) (Preprint, 2016, to appear in Ergodic Theory and Dynamical Systems) (pdf) |

38. | Uniform measures on braid monoids and dual braid monoids (with S. Abbes, V. Jugé and J. Mairesse) (Journal of Algebra 473:627-666, 2017) (pdf) |

37. | Large and moderate deviations for bounded functions of slowly mixing Markov chains (with J. Dedecker and F. Merlevède) (Preprint, 2016, to appear in Stochastics and Dynamics) (pdf) |

36. | Subadditive and multiplicative ergodic theorems (with A. Karlsson) (Preprint, 2015) (pdf) |

35. | Analyticity of the entropy and the escape rate of random walks in hyperbolic groups (Discrete Analysis2017:7, 1-37) (pdf) |

34. | Entropy and drift in word hyperbolic groups (with F. Mathéus and F. Maucourant) (Preprint, 2015) (pdf) |

33. | Subgaussian concentration inequalities for geometrically ergodic Markov chains (with J. Dedecker) (Electronic Communications in Probability 20:1-12, 2015) (pdf) |

32. | Moment bounds and concentration inequalities for slowly mixing dynamical systems (with I. Melbourne) (Electronic Journal of Probability 93:1-30, 2014) (pdf) |

31. | A numerical lower bound for the spectral radius of random walks on surface groups (Combinatorics, Probability and Computing 24: 838-856, 2015) (pdf) |

30. | Martin boundary of random walks with unbounded jumps in hyperbolic groups (Annals of Probability 43:2374-2404, 2015) (pdf) |

29. | Sharp lower bounds for the asymptotic entropy of symmetric random walks (with F. Mathéus and F. Maucourant) (Groups, Geometry, and Dynamics 9:711-735, 2015) (pdf) |

28. | Local limit theorem for symmetric random walks in Gromov-hyperbolic groups (Journal of the A.M.S. 27:893-928, 2014) (pdf) |

27. | Optimal concentration inequalities for dynamical systems (with J.-R. Chazottes) (Communications in Mathematical Physics 316:843-889, 2012) (pdf) |

26. | Correlation asymptotics from large deviations in dynamical systems with infinite measure (Colloquium Mathematicum 125:193-212, 2011) (pdf) |

25. | Random walks on co-compact Fuchsian groups (with S. Lalley) (Annales Scientifiques de l'ENS 46:129-173, 2013) (pdf) |

24. | The almost sure invariance principle for unbounded functions of expanding maps (with J. Dedecker and F. Merlevède) (ALEA 9:141-163, 2012) (pdf) |

23. | Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow (with A. Avila) (Annals of Mathematics 178:385-442, 2013) (pdf) |

22. | Banach spaces for piecewise cone hyperbolic maps (with V. Baladi) (Journal of Modern Dynamics 4:91-137, 2010) (pdf) |

21. | Almost sure invariance principle for dynamical systems by spectral methods (Annals of Probability 38:1639-1671, 2010) (pdf) |

20. | Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains (with J. Dedecker and F. Merlevède) (Annales de l'IHP Probabilités et Statistiques 46:796-821, 2010) (pdf) |

19. | Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps (Israel Journal of Mathematics 180:1-41, 2010) (pdf) |

18. | An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functions (Discrete and Continuous Dynamical Systems 24:1205-1208, 2009) (pdf) |

17. | Good Banach spaces for piecewise hyperbolic maps via interpolation (with V. Baladi) (Annales de l'IHP Analyse non linéaire 26:1453-1481, 2009) (pdf) |

16. | A Borel-Cantelli lemma for intermittent interval maps (Nonlinearity 20:1491-1497, 2007) (pdf) |

15. | Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences (Duke Mathematical Journal 147:192-284, 2009) (pdf) |

14. | Limit theorems for coupled interval maps (with J.-B. Bardet and G. Keller) (Stochastics and Dynamics 7:17-36, 2007) (pdf) |

13. | Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties (with C. Liverani) (Journal of Differential Geometry, 79:433-477, 2008) (pdf) |

12. | On almost-sure versions of classical limit theorems for dynamical systems (with J.-R. Chazottes) ( Probability Theory and Related Fields 138:195-234, 2007) ( pdf) |

11. | Exponential mixing for the Teichmüller flow (with A. Avila and J.-C. Yoccoz) (Publications mathématiques de l'IHES 104:143-211, 2006) (pdf) |

10. | Smoothness of solenoidal attractors (with A. Avila and M. Tsujii) (Discrete and Continuous Dynamical Systems 15:21-35, 2006) (pdf) |

9. | Limit theorems in the stadium billiard (with P. Bálint) (Communications in Mathematical Physics 263:451-512, 2006) (pdf) |

8. | Regularity of coboundaries for non uniformly expanding Markov maps (Proceedings of the American Mathematical Society 134:391-401, 2006) (pdf) |

7. | Banach spaces adapted to Anosov systems (with C. Liverani) (Ergodic Theory and Dynamical Systems 26:189-217, 2006) (pdf) |

6. | Decay of correlations for nonuniformly expanding systems (Bulletin de la Société Mathématique de France 134:1-31, 2006) (pdf) |

5. | Statistical properties of a skew product with a curve of neutral points (Ergodic Theory and Dynamical Systems 27:123-151, 2007) (pdf) |

4. | Berry-Esseen theorem and local limit theorem for non uniformly expanding maps (Annales de l'IHP Probabilités et Statistiques 41:997-1024, 2005) (pdf) |

3. | Central limit theorem and stable laws for intermittent maps (Probability Theory and Related Fields 128:82-122, 2004) (pdf) |

2. | Sharp polynomial estimates for the decay of correlations (Israel Journal of Mathematics 139:29-65, 2004) (pdf) |

1. | Spectre de l'opérateur de transfert en dimension 1 (Manuscripta Mathematica 106:365-403, 2001) (pdf) |

6. | Spectre du flot géodésique en courbure négative, d'après F. Faure et M. Tsujii (Astérisque 380:325-353, 2016, Séminaire Bourbaki. Vol. 2014/2015 (2016), exposé 1098) (pdf) |

5. | Limit theorems in dynamical systems using the spectral method (pdf) |

4. | Mon habilitation à diriger des recherches "Comportement quantitatif de certains systèmes dynamiques. Exemples et applications" (pdf) |

3. | Stable laws for the doubling map (pdf) |

2. | Un théorème de Kerckhoff, Masur et Smillie : Unique ergodicité sur les surfaces plates (with E. Lanneau) (Séminaires et Congrès 20:113-145, 2010) (pdf) |

1. | Ma thèse "Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes" (pdf) |

- Ergodic Theory, including Kac's Formula, Birkhoff and Kingman theorems, and culminating in the proof of my subadditive ergodic theorem with Karlsson (which is thus computer-certified).
- Properties of $L^p$ spaces, including all the basic inequalities of Hölder, Minkowski, as well as duality properties, conditional expectations, and so on.