Welcome to the home page of Patrick Cattiaux

The files attached below may differ from the published ones. The interested reader is invited to look at the final version in the corresponding journal. In case of difficulty to reach the journal or the paper inside, send me an e-mail. I shall supply you a reprint.

Some complements or corrigenda are available for some of the papers.

Preprints

1. P. Cattiaux.
   Entropy on the path space and application to singular diffusions and mean-field models. (2024) [pdf]

Published or Accepted papers

1. P. Cattiaux, F. Delebecque, O. Hacquard.
   Some flocking properties for a model of collective dynamics with topological interactions.
   To appear in Communications in Mathematical Sciences . [pdf]
2. P. Cattiaux, L. Colombani, M. Costa.
   Asymptotic deviation bounds for cumulative processes.
   Stoch. Proc. and their Appli. 163: 85–105, 2023. [pdf]
3. P. Cattiaux, A. Guillin.
   A journey with the integrated Gamma2 criterion and its weak forms.
   Geometric Aspects of Functional Analysis: Israel Seminar (GAFA). 2020-2022. LNM 2327, Springer Verlag, 167–208, 2023. [pdf]
4. P. Cattiaux, G. Conforti, I. Gentil, C. Léonard.
   Time reversal of diffusion processes under a finite entropy condition.
   Ann. Inst. Henri Poincaré Probab. Stat. 59 (4): 1844–1881, 2023 . [pdf]
5. P. Cattiaux, M. Fathi, A. Guillin.
   Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds.
   J. Math. Pures Appl. 166 (9): 1–29, 2022. [pdf]
6. P. Cattiaux, L. Colombani, M. Costa.
   Limit theorems for Hawkes processes including inhibition.
   Stoch. Proc. and their Appli. 149: 404–426, 2022. [pdf]
7. P. Cattiaux , J. Fischer, S. Roelly, S. Sindayigaya.
   Random population dynamics under catastrophic events.
   Journal of Applied Probability. 59(4): 962–982, 2022. [pdf]
8. P. Cattiaux, A. Guillin.
   Functional inequalities for perturbed measures with applications to log-concave measures and to some Bayesian problems.
   Bernoulli. 28(4): 2294–2321, 2022.  [pdf]
9. P. Cattiaux, A. Guillin, L. Wu.
   Poincaré and logarithmic Sobolev inequalities for nearly radial measures.
   Acta Math. Sinica. 38(8): 1377–1398, 2022.  [pdf]
10. P. Cattiaux, A. Guillin.
    On the Poincaré constant of log-concave measures.
    Geometric Aspects of Functional Analysis: Israel Seminar (GAFA). 2017-2019. Volume I. LNM 2256, Springer Verlag, 171–217, 2020. [pdf]
11.  P. Cattiaux, A. Guillin, P. Monmarché, C. Zhang.
    Entropic multipliers method for Langevin diffusion and weighted Log-Sobolev inequalities.
    J. of Funct. Anal. 277(11): 108288, 2019. [pdf]
12. P. Cattiaux, E. Nasreddine, M. Puel.
    Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: the critical case.
    Kinet. Relat. Models. 12(4): 727–748, 2019.  [pdf]
13. P. Cattiaux, F. Delebecque, L. Pédèches .
    Stochastic Cucker-Smale models: old and new.
    Ann. Appl. Probab. 28(5): 3239–3286, 2018. [pdf]
14. E. Boissard, P. Cattiaux, A. Guillin, L. Miclo.
    Ornstein-Uhlenbeck pinball and the Poincaré inequality in a punctured domain.
    Séminaire de Probabilités XLIX. LLNM 2215, Springer Verlag, 1–55, 2018. [pdf]
15. P. Cattiaux, J. R. Leon, C. Prieur.
    Estimation of the invariant density of a reflected diffusion using an Euler scheme.
    Monte Carlo Methods and Applications. 23(2): 71–88, 2017. [pdf]
16. P. Cattiaux, J. R. Leon, A.A. Pinedo Centeno, C. Prieur.
    An overlook on statistical inference issues for stochastic damping hamiltonian systems under the fluctuation-dissipation condition.
    Statistics: Special issue in  honour of Paul Doukhan. 51 (1) : 11–29, 2017. [pdf]
17. P. Cattiaux, A. Guillin.
    Hitting times, functional inequalities, Lyapunov conditions and uniform ergodicity. 
    J. of Funct. Anal . 272(6): 2361–2391, 2017. [pdf]
    Corrigendum Theorem 1.2  [pdf-corrigendum]
18. P. Cattiaux, L. Pédèches.
    The 2-D stochastic Keller-Segel particle model: existence and uniqueness.
    ALEA, Lat. Am. J. Probab. Math. Stat. 13 (1) : 447–463, 2016. [pdf]
19. P. Cattiaux, J. R. Leon, C. Prieur.
    Estimation for stochastic damping Hamiltonian systems under partial observations: III. Diffusion term. 
    Ann. Appl. Probab. 26 (3) : 1581–1619, 2016.  [pdf]
20. P. Cattiaux, M. Fradon, A. Kulik, S. Roelly.
    Long time behavior of stochastic hard balls systems.
    Bernoulli.  22(2) : 681–710, 2016. [pdf]
21. P. Cattiaux, J. R. Leon, C. Prieur.
    Recursive estimation for stochastic damping Hamiltonian systems.
    Journal of Nonparametric Statistics. 27 (3) : 401–424, 2015.  [pdf]
22. C. Christophe, M. Rodrigues, S.Müller, L. Dupré, P. Cattiaux, S. Gadat, S. Valitutti.
    A biased competition model theory of  cytotoxic T lymphocyte  interaction with tumor nodules. 2015.
    Plos One. Published: March 27, 2015. DOI: 10.1371/journal.pone.0120053.  [pdf]
    
23. P. Cattiaux, A. Guillin.
    Semi log-concave Markov diffusions.
    Séminaire de Probabilités XLVI. LNM 2014, Springer Verlag, 231–292, 2015. [pdf]
24. P. Cattiaux, J. R. Leon, C. Prieur.
    Estimation for stochastic damping Hamiltonian systems under partial observations: II. Drift term.
    ALEA, Lat. Am. J. Probab. Math. Stat. 11 : 359–384, 2014. [pdf]
25. P. Cattiaux, J. R. Leon, C. Prieur.
    Estimation for stochastic damping Hamiltonian systems under partial observations: I. Invariant density.
    Stoch. Proc. and their Appli. 124 (3) : 1236–1260, 2014.  [pdf]
26. P. Cattiaux.
    Long time behavior of Markov processes.
    ESAIM Proc. 44 : 110–129, 2014. [pdf]
27. P. Cattiaux, M. Manou-Abi.
    Limit theorems for some functionals with heavy tails of a discrete time Markov chain.
    ESAIM PS. 18 : 468–482, 2014. [pdf]
28. P. Cattiaux, A. Guillin.
    Functional Inequalities via Lyapunov conditions.
    In « Optimal transportation. Theory and applications. »
    London Mathematical Society Lecture Notes Series 413:274–287. Cambridge Univ. Press, 2014.
    [pdf]
29. P. Cattiaux, A. Guillin, P.A. Zitt.
    Poincaré  inequality and hitting times.
    Ann. Institut Henri Poincaré. 49 (1) : 95–118, 2013. [pdf]
    Corrigendum  Proposition 5.3  [pdf-corrigendum]
30. P. Cattiaux, D. Chafai, A. Guillin.
    Central Limit Theorems for additive functionals of ergodic Markov diffusions.
    ALEA, Lat. Am. J. Probab. Math. Stat. 9 (2) : 337–-382, 2012. [pdf]
31. P. Cattiaux, A. Guillin, L. Wu.
    Some remarks on weighted logarithmic Sobolev inequality.
    Indiana University Mathematics Journal. 60 (6) : 1885–1904, 2011. [pdf]
32. P. Cattiaux, A. Guillin, C. Roberto.
    Poincaré inequality and the L^p convergence of semi-groups.
    Elec. Comm. in Prob. 15 : 270–280, 2010. [pdf]
33. P. Cattiaux, D. Chafai, S. Motsch.
    Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model.
    Asymptotic Analysis. 67 (1-2) : 17–31, 2010.  [pdf]
34. P. Cattiaux , N. Gozlan , A. Guillin, C. Roberto.
    Functional inequalities for heavy tails distributions and application to isoperimetry.
    Electronic J. of Proba. 15 : 346–385, 2010. [pdf]
35. P. Cattiaux, A. Guillin, L. Wu.
    A remark on Talagrand’s transportation information inequality and logarithmic Sobolev inequality.
    Prob. Theory. and Rel. Fields. 148 : 285–304, 2010. [pdf]
36. P. Cattiaux, S. Méléard.
    Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned to non extinction.
    J. Math. Biology. 60 (6) : 797–829, 2010. [pdf]
37. P. Cattiaux, A. Guillin, F. Y. Wang, L. Wu.
    Lyapunov conditions for super Poincaré  inequalities.
    J. of Funct. Analysis. 256 : 1821–1841, 2009. [pdf]
38. P. Cattiaux, P. Collet, A. Lambert, S. Martinez, S. Méléard, J. San Martin.
    Quasi stationary distributions and diffusion models in population dynamics.
    The Annals of Probability, 37 (5) : 1926–1969, 2009. [pdf]
39. P. Cattiaux, A. Guillin.
    Trends to equilibrium in total variation distance.
    Ann.Institut Henri Poincaré, 45 (1) : 117–145, 2009. [pdf]
40. P. Cattiaux, P. Dai Pra, S. Roelly.
    A Constructive Approach to a Class of Ergodic HJB Equations with unbounded and non smooth Cost.
    SIAM J. Control Optim. 47 (5) : 2598–2615, 2008. [pdf]
41.  D. Bakry, F. Barthe, P. Cattiaux, A. Guillin.
    A simple proof of the Poincaré inequality in a large class of probability measures including log-concave cases. 
    Elec. Comm. Prob. 13 : 60–66, 2008. [pdf]
42. D. Bakry, P. Cattiaux, A. Guillin.
    Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré.
    J. of Funct. Analysis. 254 : 727–759, 2008. [pdf]
    Complement on Theorem 1.2 and Theorem 1.3  [pdf-complement]
43. P. Cattiaux,  A. Guillin, F. Malrieu.
    Uniform transportation inequalities and concentration for particular approximation of granular media equations.
    Prob. Theory and Rel. Fields. 140 : 19–40, 2008. [pdf]
    The final Proposition 4.3 is incorrect.
44. P. Cattiaux, A. Guillin.
    Deviation bounds for additive functionals of Markov processes.
    ESAIM PS. 12 : 12–29, 2008. [pdf]
45. F. Barthe, P. Cattiaux, C. Roberto.
    Isoperimetry between exponential and Gaussian.
    Electronic J. Proba. 12 : 1212–1237, 2007. [pdf]
46. P. Cattiaux, I. Gentil, A. Guillin.
    Weak logarithmic-Sobolev inequalities and entropic convergence.
    Prob. Theory and Rel. Fields. 139 : 563–603, 2007. [pdf]
47. P. Cattiaux, N. Gozlan.
    Deviations bounds and conditional principles for thin sets.
    Stoch. Proc. and their Appli. 117 : 221-250, 2007. [pdf]
48.  F. Barthe, P. Cattiaux, C. Roberto.
    Interpolated inequalities between exponential and gaussian, Orlicz hypercontractivity and application to isoperimetry.
    Revista Matematica Iberoamericana. 22 : 993–1066, 2006. [pdf]
49. P. Cattiaux, A. Guillin.
    On quadratic transportation cost inequalities.
    J. Math.Pures Appl. 86 : 342–361, 2006. [pdf]
50. F. Barthe, P. Cattiaux, C. Roberto.
    Concentration for independent random variables with heavy tails.
    AMRX 2005(2): 39–60, 2005. [pdf]
51. P. Cattiaux.
    Hypercontractivity for perturbed diffusion semigroups.
    Ann. Fac. Sciences Toulouse Math. (6) 14 (4):609–628, 2005. [pdf]
52. P. Cattiaux.
    A pathwise approach of some classical inequalities.
    Potential Analysis 20:361–394, 2004. [pdf]
53. P. Cattiaux, L. Mesnager.
    Hypoelliptic non-homogeneous diffusions.
    Prob. Theory and Rel. Fields 123:453–483, 2002. [pdf]
    Complement [pdf-complement]
54. P. Cattiaux, F. Gamboa.
    Large deviations and variational theorems for marginal problems.
    Bernoulli 5:81–108, 1999. [pdf]
55. P. Cattiaux, M. Fradon.
    Entropy, reversible diffusion processes and Markov uniqueness.
    J. Funct. Anal. 138:243–272, 1996.
56. P. Cattiaux, S. Roelly, H. Zessin.
    Une approche gibbsienne des diffusions browniennes infini-dimensionelles.
    Prob. Theory and Rel. Fields 104:147–179, 1996.
57. P. Cattiaux, C. Léonard.
    Minimization of the Kullback Information for General Markov Processes.
    Séminaire de Probabilités XXX. LNM 1626, Springer Verlag, 283–311, 1996.
58. P. Cattiaux, C. Léonard.
    Large deviations and Nelson Processes.
    Forum Mathematicum 7:95–115, 1995.
59. P. Cattiaux, C. Léonard.
    Minimization of the Kullback Information of Diffusion Processes.
    Ann. Inst. Henri Poincaré   30:83–132, 1994 and correction Ann. Inst. Henri Poincaré 31:705-707, 1995.
60. P. Cattiaux.
    Stochastic calculus and degenerate boundary value problems. 
    Ann. Institut Fourier, 42:541–624, 1992. [pdf]
61. P. Cattiaux.
    Calcul stochastique et opérateurs dégénérés du second ordre{II}. Problème de Dirichlet.
    Bull. Sciences. Math., 115:81–122, 1991.
62. P. Cattiaux, J.P. Lepeltier.
    Existence of a quasi Markov Nash equilibrium for non-zero sum Markov stopping games.
    Stochastics and Stoch. Rep. 30:85-103, 1990.
63. P. Cattiaux.
    Calcul stochastique et opérateurs dégénérés du second ordre{I}. Résolvantes et théorème de Hörmander.
    Bull. Sciences. Math., 114:421–462, 1990.
64. P. Cattiaux.
    Time reversal of diffusion processes with a boundary condition.
    Stoch.Proc. and their Appli. 28:275-292, 1988.
65. P. Cattiaux.
    Régularité au bord pour les densités et les densités conditionnelles d’une diffusion réfléchie hypoelliptique. 
    Stochastics and Stoch. Rep., 20:309–340, 1987.
66. P. Cattiaux. 
    Hypoellipticité et hypoellipticité partielle pour les diffusions avec une condition frontière.
    Ann. Institut Henri Poincaré, 22:67–112, 1986.

Unpublished papers and some lecture notes

1. Lectures given in Turku on Functional Inequalities. (2005).
2. Lectures given in Wuhan on Singular Diffusions. (2001). [pdf]
3. P. Cattiaux, F. Petit. Singular diffusions, time reversal and applications to Fokker-Planck equations. (2001). [pdf]
4. P. Cattiaux, C. Christophe, S. Gadat.
   A stochastic model for Cytotoxic T. Lymphocyte interaction with tumor nodules. (2016). [pdf]