Table of Contents
Page personnelle de Lorenzo Zambotti
Professeur à Sorbonne Université (ex UPMC)
Laboratoire de Probabilités, Statistique et Modèlisation (LPSM UMR 8001), case 188 - 4 pl. Jussieu, 75252 Paris Cedex 05, France
e-mail : zambotti (of course at) lpsm (dot) paris
Directeur du LPSM
Junior member of the Institut Universitaire de France (2012-2017)
From 2021 associate editor of PTRF and SPA
From 2011 to 2016 main editor, together with Thierry Bodineau, of the Annales de l'Institut Henri Poincaré, Probabilités et Statistique
From 2006 to 2011, Associate editor of Potential Analysis
From 2011 to 2013, Professeur à temps partiel à l'ENS rue d'Ulm, Paris
De 2011 à 2015, Membre du comité de pilotage de la Fondation Sciences Mathématiques de Paris
Enseignement
Cours “Probabilités et Finance” du Master 2 https://finance.math.upmc.fr/
A l'examen il sera permis de consulter le poly, plus une feuille manuscrite de synthèse, mais pas d'autres documents.
Horaires : https://finance.math.upmc.fr/calendrier/calendrier/
Voici le poly
Voici le TD0 avec des exercices préliminaires et des rappels
Voici le TD1
Voici le TD2
Voici le TD3
Voici le TD4
Voici le TD5
Voici le TD6
Voici le TD7
St-Flour slides
Research interests
- Stochastic (partial) differential equations
- Regularity Structures
- Rough Paths
- Random polymers
- Large deviations
- Heat conduction models
- Neural complexity
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.
ANR LSD - Large Stochastic Dynamical Models
in Non-Equilibrium Statistical Physics
. Projet Blanc 2016-2020. Membre.
Publications
The Sewing lemma for 0<γ≤1, arXiv preprint.
Geometric stochastic heat equations, Journal of the American Mathematical Society, Volume 35, Number 1, January 2022, Pages 1–80.
A Microlocal Approach to Renormalization in Stochastic PDEs, to appear in Communications in Contemporary Mathematics, arxiv preprint 2009.07640.
Wick polynomials in non-commutative probability, to appear in Canadian J. Math., arxiv preprint 2001.03808.
A brief and personal history of stochastic partial differential equations, DCDS.
The geometry of the space of branched Rough Paths, Proc. Lond. Math. Soc. (3) 121, no. 2, 220–251.
Bessel SPDEs and renormalized local times, Probab. Theory Related Fields 176, no. 3-4, 757–807..
Algebraic renormalisation of regularity structures, Inventiones Mathematicae, Volume 215, Issue 3, pp 1039–1156.
A Hopf-algebraic approach to cumulants-moments relations and Wick polynomials, Int. Math. Res. Not. IMRN (2020), no. 24, 10064–10099.
SPDEs and renormalisation, Stochastic partial differential equations and related fields, 271–277, Springer Proc. Math. Stat., 229, Springer.
Random Obstacle Problems, École d'Été de Probabilités de Saint-Flour XLV - 2015, Lecture Notes in Mathematics 2181, Springer.
Large deviations for the empirical measure of heavy tailed Markov renewal processes, Advances in Applied Probability, Volume 48, Issue 3, September 2016, pp. 648-671.
Hitting properties and non-uniqueness for SDE driven by stable processes, Stochastic Processes and their Applications, vol. 125, pp. 918-940.
A renewal version of the Sanov theorem, Electronic Communications in Probability, vol. 19, article 69.
L'équation de Kardar-Parisi-Zhang, Séminaire Bourbaki, Astérisque 361.
On Exceptional Times for generalized Fleming-Viot Processes with Mutations
Stochastic Partial Differential Equations: Analysis and Computations, Volume 2, Issue 1, pp 84-120.
A skew stochastic heat equation, Journal of Theoretical Probability: Volume 27, Issue 1, 168-201.
Large deviations for a random speed particle, ALEA Vol. IX, pages 739-760.
Approximate maximizers of intricacy functionals,
Probability Theory and Related Fields, Volume 153, Numbers 3-4, 421-440.
Mean mutual information and symmetry breaking for finite random fields,
Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 48, No. 2, 343–367.
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.
