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 de 2018 à 2024

Junior (2012-2017) and senior (2025-2030) member of the Institut Universitaire de France

Editor in chief of PTRF

From 2021 to 2024 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

Cours “Rough Paths and EDS” du master PMA https://www.lpsm.paris/masters/modale/index

Voici les Lectures notes (version du 14/05/25, à utiliser pour préparer l'examen)

Examen écrit : lundi 4/5/26, 13h-16h, salle 15/25 101 à Jussieu. Seul document admis : une page A4 manuscrite de synthèse.

Program détaillé pour l'examen : Chapitres 1-6. Chapitre 7 : sections 7.1, 7.2, 7.3, 7.4. Chapitre 8 : sections 8.1, 8.3, 8.4, 8.5, 8.6, 8.7. Chapitre 9.

Written exam: Monday May 4th 2026, 1pm-4pm, room 15/25 101 in Jussieu. Every student will have the right to consult only a handwritten A4 sheet of paper with a summary of results of the course.

Detailed programme for the exam: Chapters 1-6. Chapter 7 : sections 7.1, 7.2, 7.3, 7.4. Chapter 8 : sections 8.1, 8.3, 8.4, 8.5, 8.6, 8.7. Chapter 9.

Deux minicours avancés : 3-5 June https://analysis-spdes-sorbonne.github.io/

• Stochastic (partial) differential equations
• Regularity Structures
• Rough Paths
• Random polymers
• Large deviations
• Heat conduction models
• Neural complexity

* Said Karim Bounebache

* Raoul Normand-Lambert

* Eric Luçon

* Julien Reygner

* Yvain Bruned

* Nikolas Tapia

* Olga Lopusanschi

* Henri Elad-Altman

* Carlo Bellingeri

* Florian Bechtold

* Lucas Broux

* David Lee

* Jean-David Jacques

• Cyril Labbé, Benoît Laslier, Fabio Toninelli, Lorenzo Zambotti (2024), Convergence of dynamical stationary fluctuations, arXiv preprint.

• Jean-David Jacques, Lorenzo Zambotti (2025), Post-Lie algebras of derivations and regularity structures, J. Comb. Algebra.

• Lucas Broux, Francesco Caravenna, Lorenzo Zambotti (2024), Hairer's multilevel Schauder estimates without Regularity Structures, Trans. Amer. Math. Soc. 377, 6981-7035.

• Francesco Caravenna, Matteo Trabattoni, Lorenzo Zambotti (2024), On Davie's non-existence and non-uniqueness examples for equations driven by rough paths, submitted to a Proceedings volume after the second Lie-Størmer Colloquium in Oslo, Birkhäuser Springer.

• Lucas Broux, Francesco Caravenna, Lorenzo Zambotti (2023), An example of singular elliptic stochastic PDE, Mat. Contemp. 58, 3–67.

• Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia, Lorenzo Zambotti (2023), Shifted substitution in non-commutative multivariate power series with a view toward free probability, SIGMA Symmetry Integrability Geom. Methods Appl. 19, Paper No. 038.

• Lucas Broux, Lorenzo Zambotti (2022), The Sewing lemma for 0<γ≤1, J. Funct. Anal. 283, no. 10.

• Yvain Bruned, Franck Gabriel, Martin Hairer, Lorenzo Zambotti (2022), Geometric stochastic heat equations, Journal of the American Mathematical Society, Volume 35, Number 1, January 2022, Pages 1–80.

• Claudio Dappiaggi, Nicolò Drago, Paolo Rinaldi, Lorenzo Zambotti (2020), A Microlocal Approach to Renormalization in Stochastic PDEs, to appear in Communications in Contemporary Mathematics, arxiv preprint 2009.07640.

• Francesco Caravenna, Lorenzo Zambotti (2020), Hairer's Reconstruction Theorem without Regularity Structures, EMS Surv. Math. Sci. 7 (2020), no. 2, 207–251.

• Lucas Broux, Francesco Caravenna, Lorenzo Zambotti (2022), An introduction to the analytic theory of Regularity Structures, Submitted to ESI Lecture Notes series (EMS Press).

• K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti (2020), Wick polynomials in non-commutative probability, to appear in Canadian J. Math., arxiv preprint 2001.03808.

• Lorenzo Zambotti (2020), A brief and personal history of stochastic partial differential equations, DCDS.

• N. Tapia, L. Zambotti (2020), The geometry of the space of branched Rough Paths, Proc. Lond. Math. Soc. (3) 121, no. 2, 220–251.

• H. Elad Altman, L. Zambotti (2020), Bessel SPDEs and renormalized local times, Probab. Theory Related Fields 176, no. 3-4, 757–807.

• Yvain Bruned, Martin Hairer, Lorenzo Zambotti (2019), Algebraic renormalisation of regularity structures, Inventiones Mathematicae, Volume 215, Issue 3, pp 1039–1156.

• K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti (2018), A Hopf-algebraic approach to cumulants-moments relations and Wick polynomials, Int. Math. Res. Not. IMRN (2020), no. 24, 10064–10099.

• L. Zambotti (2018), SPDEs and renormalisation, Stochastic partial differential equations and related fields, 271–277, Springer Proc. Math. Stat., 229, Springer.

• Lorenzo Zambotti (2017), Random Obstacle Problems, École d'Été de Probabilités de Saint-Flour XLV - 2015, Lecture Notes in Mathematics 2181, Springer.

• Mauro Mariani, Lorenzo Zambotti (2016), 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.

• Julien Berestycki, Leif Doering, Leonid Mytnik, L. Zambotti, (2015), Hitting properties and non-uniqueness for SDE driven by stable processes, Stochastic Processes and their Applications, vol. 125, pp. 918-940.

• Mauro Mariani, Lorenzo Zambotti (2014), A renewal version of the Sanov theorem, Electronic Communications in Probability, vol. 19, article 69.

• L. Zambotti (2014), L'équation de Kardar-Parisi-Zhang, Séminaire Bourbaki, Astérisque 361.

• Julien Berestycki, Leif Doering, Leonid Mytnik, L. Zambotti, (2014), On Exceptional Times for generalized Fleming-Viot Processes with Mutations Stochastic Partial Differential Equations: Analysis and Computations, Volume 2, Issue 1, pp 84-120.

• Said Karim Bounebache, L. Zambotti, (2014), A skew stochastic heat equation, Journal of Theoretical Probability: Volume 27, Issue 1, 168-201.

• R. Lefevere, M. Mariani, L. Zambotti, (2012)Large deviations for a random speed particle, ALEA Vol. IX, pages 739-760.

• J. Buzzi, L. Zambotti, (2012) Approximate maximizers of intricacy functionals, Probability Theory and Related Fields, Volume 153, Numbers 3-4, 421-440.

• J. Buzzi, L. Zambotti, (2012) 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.

• R. Lefevere, M. Mariani, L. Zambotti, (2011) Large deviations for renewal processes, Stochastic Processes and Their Applications, Volume 121, Issue 10, 2243-2271.

• R. Lefevere, M. Mariani,L. Zambotti, (2011) Large deviations of the current in stochastic collisional dynamics, J. Math. Phys. 52, no. 3.

• R. Normand, L. Zambotti (2011), Uniqueness of post-gelation solutions of a class of coagulation equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 28, no. 2, 189-215.

• R. Lefevere, M. Mariani,L. Zambotti, (2010) Macroscopic fluctuations theory of aerogel dynamics, Journal of Statistical Mechanics, Vol. 2010, Issue 12.

• R. Lefevere,L. Zambotti, (2010) Hot scatterers and tracers for the transfer of heat in collisional dynamics, J. Stat. Phys. Volume 139, 4, Page 686–713.

• L. Ambrosio, G. Savaré, L. Zambotti, (2009) Existence and Stability for Fokker-Planck equations with log-concave reference measure, Probability Theory and Related Fields, vol. 145, 517-564.

• L. Zambotti, (2008) Fluctuations for a conservative interface model on a wall, ALEA, vol. 4, pp. 167-184.

• L. Zambotti, (2008) A conservative evolution of the Brownian excursion, Electronic Journal of Probability, vol. 13, 1096-1119.

• Max-K. Von Renesse, M. Yor, L. Zambotti, (2008) Quasi-invariance properties of a class of subordinators, Stochastic Processes and Their Applications, vol. 188 no. 1, 2038-2057.

• F. Caravenna, G. Giacomin, L. Zambotti, (2007) Infinite volume limits of polymer chains with periodic charges, Markov Processes and Related Fields, vol. 13, no. 4, 697-730.

• F. Caravenna, G.Giacomin, L. Zambotti, (2007) A renewal theory approach to periodic copolymers with adsorption, Annals of Applied Probability, vol. 17, no. 4, 1362-1398.

• A. Debussche, L. Zambotti, (2007) Conservative Stochastic Cahn-Hilliard equation with reflection, Annals of Probability, vol. 35, no. 5, 1706-1739.

• L. Zambotti, (2006) Convergence of approximations of monotone gradient systems, Journal of Evolution Equations, 6(4), 601-619.

• F. Caravenna, G. Giacomin, L. Zambotti, (2006) Sharp asymptotic behavior for wetting models in (1+1)-dimension, Electronic Journal of Probability, 11, 345-362.

• Robert C. Dalang, Carl Mueller, L. Zambotti, (2006) Hitting properties of parabolic s.p.d.e.'s with reflection. Annals of Probability, 34 n. 4, 1423-1450.

• L. Zambotti, (2005) 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.

• J.-D. Deuschel, G. Giacomin, L. Zambotti, (2005) Scaling limits of equilibrium wetting models in (1+1)-dimension. Prob. Theory and Rel. Fields, 132 n. 4, 471 - 500.

• L. Zambotti, (2005) Integration by parts on the law of the reflecting Brownian motion. J. Funct. Anal., 223 n. 1, 147-178.

• J.-D. Deuschel, L. Zambotti, (2005) Bismut-Elworthy's formula and random walk representation for SDEs with reflection. Stochastic Process. Appl., 115 n. 6, pp 907-925.

• M. Yor, L. Zambotti (2004) A Remark About the Norm of a Brownian Bridge, Statist. Probab. Lett., 68 n. 3, 297–304.

• L. Zambotti, (2004) Fluctuations for a \nabla\varphi interface model with repulsion from a wall, Prob. Theory and Rel. Fields, 129 n. 3, 315-339.

• L. Zambotti, (2004) Occupation densities for SPDEs with reflection, Annals of Probability, 32 n. 1A, 191-215.

• S. Bonaccorsi, L. Zambotti, (2004) Integration by parts on the Brownian Meander, Proc. Amer. Math. Soc., 132 n. 3, 875-883.

• L. Zambotti, (2003) Integration by parts on \delta-Bessel Bridges, \delta > 3, and related SPDEs, Annals of Probability, 31 n. 1, 323-348.

• L. Zambotti, (2002) Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection, Probab. Theory Related Fields, 123 n. 4, 579–600.

• L. Zambotti, (2002) Integration by parts on Bessel Bridges and related Stochastic PartialDifferential Equations, C. R. Acad. Sci. Paris, Ser. I, 334 n. 3, 209-212.

• L. Zambotti, (2001) A reflected stochastic heat equation as symmetric dynamics with respect to the 3-d Bessel bridge, J. Funct. Anal., 180 n. 1, 195–209.

• L. Zambotti, (2000) An analytic approach to existence and uniqueness for martingale problems in infinite dimensions, Probab. Theory Related Fields, 118 n. 2, 147–168.

• E. Priola, L. Zambotti, (2000) New optimal regularity results for infinite dimensional elliptic equations, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 3 n. 2, 411–429.

• L. Zambotti, (1999) Infinite-dimensional elliptic and stochastic equations with Hoelder-continuous coefficients, Stochastic Anal. Appl., 17 n. 3, 487–508.