Sébastien Gouëzel

Sébastien Gouëzel Directeur de recherche CNRS de première classe

Campus de Beaulieu, bâtiments 22 et 23
263 avenue du Général Leclerc, CS 74205
35042 RENNES Cedex

E-mail : sebastien.gouezel "at" univ-rennes1.fr
Bureau : 313
Téléphone : 02 23 23 52 97

Research articles:

50. Random walk speed is a proper function on Teichmüller space (with A. Azemar, V. Gadre, T. Haettel, P. Lessa and C. Uyanik) (Journal of Modern Dynamics 19:815-832, 2023) (pdf)
49. Minimal distance between random orbits (with J. Rousseau and M. Stadlbauer) (Preprint, 2022) (pdf)
48. Exponential bounds for random walks on hyperbolic spaces without moment conditions (Tunisian Journal of Mathematics 4:635-671, 2022) (pdf)
47. Pressure at infinity and strong positive recurrence in negative curvature (with B. Schapira and S. Tapie) (Comment. Math. Helv. 98:431-508, 2023) (pdf)
46. Classical and microlocal analysis of the X-ray transform on Anosov manifolds (with T. Lefeuvre) (Analysis & PDE 14:301-322, 2021) (pdf)
45. Boundary of the range of a random walk and the Fölner property (with G. Deligiannidis and Z. Kosloff) (Electronic Journal of Probability 26:110:1-39, 2021) (pdf)
44. A corrected quantitative version of the Morse lemma (with V. Shchur) (Journal of Functional Analysis 277:1248-1258, 2019) (pdf)
43. Ruelle spectrum of linear pseudo-Anosov maps (with F. Faure and E. Lanneau) (Journal de l'École Polytechnique 6:811-877, 2019) (pdf)
42. Asymptotic combinatorics of Artin-Tits monoids and of some other monoids (with S. Abbes, V. Jugé and J. Mairesse) (Journal of Algebra 525:497-561, 2019) (pdf)
41. Growth of normalizing sequences in limit theorems for conservative maps (Electronic Communications in Probability 23-99, 2018) (pdf)
40. Variations around Eagleson's Theorem on mixing limit theorems for dynamical systems (Ergodic Theory and Dynamical Systems 40, 3368-3374, 2020) (pdf)
39. Quantitative Pesin theory for Anosov diffeomorphisms and flows (with L. Stoyanov) (Ergodic Theory and Dynamical Systems 39:159-200, 2019) (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) (Stochastics and Dynamics 18:1850017, 2018) (pdf)
36. Subadditive and multiplicative ergodic theorems (with A. Karlsson) (Journal of the EMS 22:1893-1915, 2020) (pdf)
35. Analyticity of the entropy and the escape rate of random walks in hyperbolic groups (Discrete Analysis 2017:7, 1-37) (pdf)
34. Entropy and drift in word hyperbolic groups (with F. Mathéus and F. Maucourant) (Inventiones Mathematicae 211:1201-1255, 2018) (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)

Other documents:

9. Subadditive cocycles and horofunctions (Talk at the ICM 2018) (pdf)
8. Méthodes entropiques pour les convolutions de Bernoulli, d'après Hochman, Shmerkin, Breuillard, Varjú (exposé au séminaire Bourbaki 2018) (pdf)
7. Cocycles sous-additifs et horofonctions (Séminaires et Congrès 31:19-38, 2017) (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 (Proceedings of Symposia in Pure Mathematics 89:161-193, 2015) (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 de doctorat "Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes" (pdf)

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 first one I have managed to use efficiently is Isabelle/HOL. In addition to several facts that have been added to the main library (for instance conditional expectations), I have developed a few theories (see below).

However, I have been stuck somewhat by the limitations of the underlying logic in Isabelle (lack of dependent types, making it hard for instance to define the $p$-adic numbers as this should be a type depending on an integer parameter $p$, and essentially impossible to define the Gromov-Hausdorff distance between compact metric spaces without redefining everything on metric spaces from scratch, and avoiding typeclasses). These limitations are also what makes Isabelle/HOL simple enough to provide much better automation than in any other proof assistant, but still I decided to turn to a more recent system, Lean, which is less mature, has less libraries, and less automation, but where the underlying logic (essentially the same as in Coq) is stronger (and, as far as I can see, strong enough to speak in a comfortable way about all mathematical objects I am interested in). I am now a maintainer of the mathlib library in Lean.

6. A formalization of the change of variables formula for integrals in mathlib (CICM 2022, Lecture Notes in Computer Science 13467:3-18, 2022) (pdf)
5. Formalizing the Gromov-Hausdorff distance (CICM-WS 2021, CEUR-WS vol. 3377) (pdf)
4. the Gromov-Hausdorff distance (Lean 3 2019) (Link)
3. Gromov Hyperbolicity (Isabelle/HOL 2018) (Link)
2. $L^p$ spaces (Isabelle/HOL 2016) (Link)
1. Ergodic theory (Isabelle/HOL 2016) (Link)