Page personnelle de Lorenzo Zambotti
Professeur à l'UPMC
Laboratoire de Probabilités et Modèles Aléatoires (LPMA), case 188 - 4 pl. Jussieu, 75252 Paris Cedex 05, France
e-mail : lorenzo.zambotti (of course at) upmc.fr
Professeur à temps partiel à l'ENS
Département de Mathématiques et Applications (DMA) - 45 rue d'Ulm, 75230 PARIS cedex 05, France
Main editor, together with Thierry Bodineau, of the Annales de l'Institut Henri Poincaré, Probabilités et Statistique
Associate editor of Potential Analysis
Research interests
- Stochastic (partial) differential equations
- Random polymers
- Large deviations
- Heat conduction models
- Neural complexity
Enseignement
Cours “Théorèmes limites et grandes déviations” du Master 2 Probabilités et Modèles Aléatoires
Voici le sujet corrigé de l'examen du 18/01/12.
Voici le sujet corrigé du partiel.
Il sera permis de consulter une une fiche manuscrite de format A4.
Le matériel couvert en cours correspond à:
- P. Billingsley Convergence of Probability measures : Chapitre 1, sections 1, 2, 3, 5; Chapitre 2, sections 7, 8, 9; Chapitre 3, sections 12, 13, 14.
- F. Den Hollander Large deviations : Chapitre I, sections 1, 2, 3, 4, 5; Chapitre III, sections 1, 2; Chapitre IV, sections 1,2,3; Chapitre V, sections 1, 2, 3, 4.
- A. Dembo, O. Zeitouni Large deviations techniques : Chapitre 5, section 2; Théorème 5.6.3.
Voici les Feuilles de TD: TD1, TD2, TD3, TD4, TD5, TD6, TD7
Voici le sujet d'examen de l'année 2010-11 (donné par le responsable du cours de l'année dernière).
Cours de C/C++
TP noté n. 1 de l'année passée : Exam1
CV
Here is my CV : in French and in English
Grants
ANR ECRU - Explorations on rough paths. Projet Blanc 2009-2012. Membre.
ANR SHEPI - Interacting Particle Systems Out of Equilibrium. Projet Blanc 2011-2014. Membre.
Publications
Hitting properties and non-uniqueness for SDE driven by stable processes, preprint.
A skew stochastic heat equation, preprint.
Large deviations for a random speed particle, preprint.
Approximate maximizers of intricacy functionals,
to appear in Probability Theory and Related Fields.
Mean mutual information and symmetry breaking for finite random fields,
to appear in Annales de l'IHP (B) Probabilités et Statistique.
Large deviations for renewal processes,
Stochastic Processes and Their Applications, Volume 121, Issue 10, 2243-2271.
Large deviations of the current in stochastic collisional dynamics,
J. Math. Phys. 52, no. 3.
Uniqueness of post-gelation solutions of a class of coagulation equations,
Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 28, no. 2, 189-215.
Macroscopic fluctuations theory of aerogel dynamics,
Journal of Statistical Mechanics, Vol. 2010, Issue 12.
Hot scatterers and tracers for the transfer of heat in collisional dynamics,
J. Stat. Phys. Volume 139, 4, Page 686--713.
Existence and Stability for Fokker-Planck equations with log-concave reference measure,
Probability Theory and Related Fields, vol. 145, 517-564.
Fluctuations for a conservative interface model on a wall,
ALEA, vol. 4, pp. 167-184.
A conservative evolution of the Brownian excursion,
Electronic Journal of Probability, vol. 13, 1096-1119.
Quasi-invariance properties of a class of subordinators,
Stochastic Processes and Their Applications, vol. 188 no. 1, 2038-2057.
Infinite volume limits of polymer chains with periodic charges,
Markov Processes and Related Fields, vol. 13, no. 4, 697-730.
A renewal theory approach to periodic copolymers with adsorption,
Annals of Applied Probability, vol. 17, no. 4, 1362-1398.
Conservative Stochastic Cahn-Hilliard equation with reflection,
Annals of Probability, vol. 35, no. 5, 1706-1739.
Convergence of approximations of monotone gradient systems,
Journal of Evolution Equations, 6(4), 601-619.
Sharp asymptotic behavior for wetting models in (1+1)-dimension,
Electronic Journal of Probability, 11, 345-362.
Hitting properties of parabolic s.p.d.e.'s with reflection.
Annals of Probability, 34 n. 4, 1423-1450.
Ito-Tanaka's formula for SPDEs driven by additive space-time white noise,
in Stochastic Partial Differential Equations and Applications - VII,
edited by G. Da Prato and L. Tubaro, pp. 337-347, Taylor & Francis Group.
Scaling limits of equilibrium wetting models in (1+1)-dimension.
Prob. Theory and Rel. Fields, 132 n. 4, 471 - 500.
Integration by parts on the law of the reflecting Brownian motion.
J. Funct. Anal., 223 n. 1, 147-178.
Bismut-Elworthy's formula and random walk representation for SDEs with reflection.
Stochastic Process. Appl., 115 n. 6, pp 907-925.
A Remark About the Norm of a Brownian Bridge,
Statist. Probab. Lett., 68 n. 3, 297--304.
Fluctuations for a \nabla\varphi interface model with repulsion from a wall,
Prob. Theory and Rel. Fields, 129 n. 3, 315-339.
Occupation densities for SPDEs with reflection,
Annals of Probability, 32 n. 1A, 191-215.
Integration by parts on the Brownian Meander,
Proc. Amer. Math. Soc., 132 n. 3, 875-883.
Integration by parts on \delta-Bessel Bridges, \delta > 3, and related SPDEs,
Annals of Probability, 31 n. 1, 323-348.
Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection,
Probab. Theory Related Fields, 123 n. 4, 579--600.
Integration by parts on Bessel Bridges and related Stochastic Partial Differential Equations,
C. R. Acad. Sci. Paris, Ser. I, 334 n. 3, 209-212.
A reflected stochastic heat equation as symmetric dynamics with respect to the 3-d Bessel bridge,
J. Funct. Anal., 180 n. 1, 195--209.
An analytic approach to existence and uniqueness for martingale problems in infinite dimensions,
Probab. Theory Related Fields, 118 n. 2, 147--168.
New optimal regularity results for infinite dimensional elliptic equations,
Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 3 n. 2, 411--429.
Infinite-dimensional elliptic and stochastic equations with Hoelder-continuous coefficients,
Stochastic Anal. Appl., 17 n. 3, 487--508.
