Page web de Jean-René Chazottes

Financements sur projet actuels

• Projet 80PRIME 2023 "Vers une écologie probabiliste : des événements d’interaction entre individus aux populations", avec V. Bansaye (CMAP, École polytechnique) et S. Billiard (Évo-Éco-Paléo, Université de Lille). 

• International Research Project (CNRS), France-Brésil, 2024-2028, coordonné par Didina Serban (IPhT).

• Projet financé par la FAPESP, 2023-2025, "Stochastic processes on discrete structures: statistical properties, inference and criticality" (coordonné par S. Gallo, Université de São Carlos, Brésil). 

Enseignement (2009-2021)

J'ai été professeur chargé de cours à temps partiel au Département de Mathématiques Appliquées de l'École polytechnique pendant douze années, entre 2009 et 2021.

J'ai donné les petites classes du cours de tronc commun sur les Probabilités, et celles du cours Chaînes de Markov et martingales en temps discret (cours de seconde année). J'ai également enseigné un cours en troisième année (cours intitulé Modélisation mathématique en écologie).

Mon recueil d'exercices corrigés de probabilités de première année est disponible sur demande (349 pages actuellement).

J'ai également participé à l'élaboration d'un MOOC (ou FLOT) diffusé sur la plateforme Coursera : Aléatoire : une introduction aux probabilités (avec Sylvie Méléard et Carl Graham) [Partie 1 / Partie 2]

Une sélection (subjective) de mes publications (articles de recherche)

• Large population limit of the spectrum of killed birth-and-death processes, avec P. Collet et S. Méléard,  44 pages, Journal of Functional Analysis 285, Issue 9 (2023).

• Gaussian concentration bounds for stochastic chains of unbounded memory, avec S. Gallo et D. Takahashi (40 pages). Annals of Applied Probability 33(5): 3321-3350 (2023).

• Return-time L^q-spectrum for equilibrium states for potentials with summable variation, avec M. Abadi, V. Amorim et S. Gallo, Ergodic Theory and Dynamical Systems 43 , Issue 8 (2023) , pp. 2489 - 2515.

• Gaussian concentration and uniqueness of equilibrium states in lattice systems, avec J. Moles, F. Redig et E. Ugalde. Journal of Statistical Physics 181 (2020), 2131-2149.

• Quasi-stationary distributions and resilience: what to get from a sample?, avec P. Collet, S. Martínez et S. Méléard (43 pages). Journal de l'Ecole Polytechnique 7 (2020).

• Rejuvenating functional responses with renewal theory, avec V. Bansaye et S. Billiard (31 pages). Journal of the Royal Society Interface 15 (2018).

• Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes
  with P.  Collet and Sylvie Méléard, Probab. Theory & Rel. Fields 164 (2015), issue 1, 48 pages.

• Tilings of the plane and Thurston semi-norm
  with J.-M. Gambaudo and F. Gautero, Geometriae Dedicata 173 (2014), issue 1, 14 pages.

• Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems
  with P. Collet, Ergod. Th. & Dynam. Sys. 33 (2013),  41 pages.

• Optimal concentration inequalities for dynamical systems
  with S. Gouëzel, Commun. Math. Phys. 316 (2012), 47 pages.

• On the finite-dimensional marginals of shift-invariant measures
  with J.-M. Gambaudo, M. Hochman and E. Ugalde, Ergod. Th. & Dynam. Sys. 32 (2012), 16 pages.

• On the preservation of Gibbsianness under symbol amalgamation
  with E. Ugalde, Entropy of hidden Markov processes and connections to dynamical systems, 72–97,  London Math. Soc. Lecture Note Ser., 385, Cambridge Univ. Press, Cambridge, 2011.

• Estimates of Kolmogorov complexity in approximating Cantor sets
  with C. Bonanno and P. Collet, Nonlinearity 24 (2011), pp. 459-479.

• On the zero-temperature of Gibbs states
  with M. Hochman, Commun. Math. Phys. 297 (2010), no. 1, 265-281.

• On the zero-temperature limit of one-dimensional Gibbs measures via renormalization: the case of locally constant potentials
  with J.-M. Gambaudo and E. Ugalde, Ergod. Th. & Dynam. Sys. (2010). Nota bene: there is a misprint in the example of section 6.2 in the published version. This is corrected in the version on arXiv.

• Poisson processes for subsystems of finite type in symbolic dynamics
  with Z. Coelho and P. Collet, Stoch. Dyn. 9 (2009), 30 pages.

• Coupling, concentration inequalities and stochastic dynamics
  with P. Collet, F. Redig,  J. Math. Phys 49, 125214 (2008).

• Concentration inequalities for random fields via coupling
  (with P. Collet, C. Kuelske, F. Redig), Probab. Th. & Rel. Fields 137 (2007), 25 pages.

• On almost-sure versions of classical limit theorems for dynamical systems
  (with S. Gouëzel), Probab. Th. & Rel. Fields 138 (2007) 195--234.

• Large deviations for empirical entropies of g-measures
  (with D. Gabrielli), Nonlinearity 18 (2005) 2545--2563.

• Synchronization in directionally coupled systems: some rigorous results (with V. Afraimovich and A. Cordonet), Discrete and Continuous Dynamical Systems B 1 (2001), no. 4.

Liste complète des publications (articles de recherche)

• Large population limit of the spectrum of killed birth-and-death processes, avec P. Collet et S. Méléard,  44 pages, Journal of Functional Analysis 285, Issue 9 (2023).

• Relative entropy, Gaussian concentration and uniqueness of equilibrium states, avec F. Redig, 13 pages, Entropy 2022, 24(11), 1513.

• Gaussian concentration bounds for stochastic chains of unbounded memory, avec S. Gallo et D. Takahashi (40 pages). Annals of Applied Probability 33(5): 3321-3350 (2023).

• Return-time L^q-spectrum for equilibrium states for potentials with summable variation, avec M. Abadi, V. Amorim et S. Gallo, Ergodic Theory and Dynamical Systems 43 , Issue 8 (2023) , pp. 2489 - 2515.

• Evolution of Gaussian concentration bounds under diffusions, avec P. Collet et F. Redig, 48 pages, Markov Processes and Related Fields 27 (2021), 707-754.

• Evolution of concentration under lattice spin-flip dynamics, avec P. Collet et F. Redig, 25 pages, Journal of Statistical Physics 184 (2021).

• Gaussian concentration and uniqueness of equilibrium states in lattice systems, avec J. Moles, F. Redig et E. Ugalde. Journal of Statistical Physics 181 (2020), 2131-2149.

• Quasi-stationary distributions and resilience: what to get from a sample?, avec P. Collet, S. Martínez et S. Méléard (43 pages). Journal de l'Ecole Polytechnique 7 (2020).

• Gaussian Concentration bound for potentials satisfying Walters condition with subexponential continuity rates, avec J. Moles et E. Ugalde. Nonlinearity 33 (2020).

• On time scales and quasi-stationary distributions for multitype birth-and-death processes, avec P. Collet et S. Méléard (51 pages). Ann. Inst. H. Poincaré Probab. Statist. 55 (2019).

• Rejuvenating functional responses with renewal theory, avec V. Bansaye et S. Billiard (31 pages). Journal of the Royal Society Interface 15 (2018).

• On concentration inequalities and their applications for Gibbs measures in lattice systems, with P. Collet and F. Redig, J. Stat. Phys. 169 (2017), issue 3, 58 pages.

• Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes
  with P.  Collet and Sylvie Méléard, Probab. Theory & Rel. Fields 164 (2015), issue 1, 48 pages.

• Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems
  with F. Redig. Electronic J. Probab. (2014), 27 pages.

• Tilings of the plane and Thurston semi-norm
  with J.-M. Gambaudo and F. Gautero, Geometriae Dedicata 173 (2014), issue 1, 14 pages.

• Optimal concentration inequalities for dynamical systems
  with S. Gouëzel, Commun. Math. Phys. 316 (2012), 47 pages.

• Nonconventional averages along arithmetic progressions and lattice spin systems
  with G. Carinci, C. Giardinà and F. Redig, Indag. Math. 23 (2012), 13 pages.

• Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems
  with P. Collet, Ergod. Th. & Dynam. Sys. 33 (2013),  41 pages.

• Concentration bounds for entropy estimation of one-dimensional Gibbs measures
  with C. Maldonado, Nonlinearity 24 (2011), 11 pages.

• On the finite-dimensional marginals of shift-invariant measures
  with J.-M. Gambaudo, M. Hochman and E. Ugalde, Ergod. Th. & Dynam. Sys. 32 (2012), 16 pages.

• Poincaré inequality for Markov random fields via disagreement percolation
  with F. Redig and F. Völlering, 20 pages, to appear in Indagationes Mathematicae (2011), in a special issue in the memory of F. Takens.

• On the preservation of Gibbsianness under symbol amalgamation
  with E. Ugalde, Entropy of hidden Markov processes and connections to dynamical systems, 72–97,  London Math. Soc. Lecture Note Ser., 385, Cambridge Univ. Press, Cambridge, 2011.

• Estimates of Kolmogorov complexity in approximating Cantor sets
  with C. Bonanno and P. Collet, Nonlinearity 24 (2011), pp. 459-479.

• On the zero-temperature of Gibbs states
  with M. Hochman, Commun. Math. Phys. 297 (2010), no. 1, 265-281.

• On the zero-temperature limit of one-dimensional Gibbs measures via renormalization: the case of locally constant potentials
  with J.-M. Gambaudo and E. Ugalde, Ergod. Th. & Dynam. Sys. (2010). Nota bene: there is a misprint in the example of section 6.2 in the published version. This is corrected in the version on arXiv.

• Poisson processes for subsystems of finite type in symbolic dynamics
  with Z. Coelho and P. Collet, Stoch. Dyn. 9 (2009), 30 pages.

• Concentration inequalities for Markov processes via coupling
  with F. Redig, Electron. J. Probab. 14 (2009), 19 pages.

• Coupling, concentration inequalities and stochastic dynamics
  with P. Collet, F. Redig,  J. Math. Phys 49, 125214 (2008).

• A concentration inequality for interval maps with an indifferent fixed point
  with P. Collet, F. Redig and E. Verbitskiy, Ergod. Th. Dynam. Sys. 19 (2009), 21 pages.

• Concentration inequalities for random fields via coupling
  (with P. Collet, C. Kuelske, F. Redig), Probab. Th. & Rel. Fields 137 (2007), 25 pages.

• On almost-sure versions of classical limit theorems for dynamical systems
  (with S. Gouëzel), Probab. Th. & Rel. Fields 138 (2007) 195--234.

• Relative entropy and waiting times for continuous-time Markov processes
  (with C. Giardina, F. Redig), Electron. J. Probab. 11 (2006).

• On Approximate Pattern-Matching for a Class of Gibbs Random Fields
  (with F. Redig and E. Verbitskiy), Annals of Appl. Probab. 16 (2) (2006) 670--684.

• Testing the irreversibility of a Gibssian process via hitting and return times (with F. Redig), Nonlinearity 18 (2005) 2477-2489.

• Devroye inequality for a class of non-uniformly hyperbolic dynamical systems
  (with P. Collet and B. Schmitt), Nonlinearity 18 (2005) 2323-2340.

• Statistical consequences of Devroye inequality for processes. Applications to a class of non-uniformly hyperbolic dynamical systems (with P. Collet and B. Schmitt), Nonlinearity 18 (2005) 2341-2364.

• Occurrence, repetition and matching of patterns in the low-temperature Ising model
  (with F. Redig), J. Stat. Phys. 121 (2005), Nos 3-4, 579-605.

• Large deviations for empirical entropies of g-measures
  (with D. Gabrielli), Nonlinearity 18 (2005) 2545--2563.

• Approximations and fluctuations of hitting and recurrence times for Gibbsian measures
  (with E. Ugalde), Discrete and Continuous Dynamical Systems B (2005) 5, no. 3, 565--586.

• Fluctuations of the n-th return time for Axiom A diffeomorphisms
  (with R. Leplaideur), Discrete and Continuous Dynamical Systems A (2005) 13, no. 2, 399--411.

• Finite type approximations of Gibbs measures on sofic subshifts
  (with E. Ugalde and L. Ramirez), Nonlinearity 18 (2005) 445--463.

• Almost sure central limit theorems and Erdös-Rényi type law for expanding maps of the interval (with P. Collet), Ergod. Th. & Dynam. Sys. 25 (2005), no. 2, 419--441.

• Exponential distribution for the occurrence of rare patterns in Gibssian random fields,
  Commun. Math. Phys. 246, Number 2 (2004), 269--294 (with M. Abadi, F. Redig and E. Verbitskiy).

• Local rates of Poincaré recurrence for rotations and weak mixing (with F. Durand)
  Discrete & Continuous Dynamical Systems A 12 (2005), no. 1, 175--183. (2003).

• Hitting and returning to non-rare events in mixing dynamical systems, Nonlinearity16 (2003) 1017-1034.

• Projections of Markov measures may be Gibbsian (with E. Ugalde), J. Stat. Phys. 111, Nos. 5/6, 2003.

• Pointwise dimensions for Poincaré recurrences associated with maps and special flows (with V. Afraimovich and B. Saussol), Discrete and Continuous Dynamical Systems A 9, No. 2 (2003).

• Spectra of dimensions for Poincaré recurrence for special flows (with V. Afraimovich and E. Ugalde), Taiwanese J. Math. 6, No. 2 (2002).

• On pointwise dimensions and spectra of measures (with B. Saussol), C. R. Acad. Sci. Paris, Sér. I, Vol. 333(8) (2001), pp. 719--723.

• Nonsmooth functions in chaos synchronization (with V. Afraimovich and A. Cordonet), Physics Letters A, 283 (2001), no. 1--2, 109--112.

• Multivalued functions in the generalized synchronization of chaos (with V. Afraimovich, A. Cordonet, N. Rulkov and C.T. Lewis), Physical Review E 64 (2001).

• Poincaré recurrences and entropy of suspended flows, C. R. Acad. Sc. Paris, t. 332, Série I, 1-6, 2001.

• Synchronization in directionally coupled systems: some rigorous results (with V. Afraimovich and A. Cordonet), Discrete and Continuous Dynamical Systems B 1 (2001), no. 4.

• Local dimensions associated with Poincaré recurrences (with V. Afraimovich and B. Saussol), Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 64-74.

• Dimensions and waiting times for Gibbs measures, J. Statist. Phys. 98 (2000), no. 1-2, 305--320.

• Relative entropy, dimensions and large deviations for g-measures (with E. Olivier), J. Phys. A: Math. Gen. 33 (2000), no. 4, 675--689.

• Relative entropy and identification of Gibbs measures in dynamical systems (with E. Floriani and R. Lima), J. Statist. Phys. 90(3-4) (1998) 697-725.

Bref curriculum vitæ 

Né en 1973, en Avignon, marié, trois enfants.

• 2023-présent : directeur de recherche au CNRS de première classe, CPHT, École polytechnique.

• 2017-2025 : directeur du Centre de Physique Théorique de l'Ecole polytechnique.

•  2014-2023 : directeur de recherche au CNRS de seconde classe , CPHT, École polytechnique.

• Membre élu du Conseil d'Administration de la Société Mathématique de France (2017-2020, 2020-2023).

• Habilitation à diriger des recherches (HDR) soutenue en 2010 à l'Université Paris-Sud 11 (maintenant Université Paris-Saclay).

• 2009-2021 : professeur chargé de cours à temps partiel au département de mathématiques appliquées de l'École polytechnique.

• 2001-2014 : chargé de recherche au CNRS au CPHT à l'École polytechnique.

• 2000-2001 : postdoc au Brésil (IME, São Paulo, Brésil, avec A. Galves).

• 1999-2000 : postdoc au Mexique (IICO, San Luis Potosí, Mexique, avec V. Afraimovich).

• 1996-1999 : thèse de doctorat (sous la dir. de R. Lima). Spécialité : physique théorique & mathématique, Centre de Physique Théorique, Marseille).

• 1995-1996 : DEA (spécialité : physique théorique & mathématique, physique des particules & astrophysique, Centre de Physique Théorique, Marseille).

• 1994-1995 : maîtrise de physique fondamentale à l'université de Provence, Marseille.

• 1993-1994 : licence de physique fondamentale à l'université de Provence, Marseille.

• 1991-1993 : deug a (spécialité : science & structure de la matière) à l'université de la Méditerranée, Marseille.