====== Page personnelle de Lorenzo Zambotti ====== {{ foto.jpg?210x220}} **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 [[https://www.springer.com/journal/440|PTRF]] and [[https://www.journals.elsevier.com/stochastic-processes-and-their-applications|SPA]] From 2011 to 2016 main editor, together with [[http://www.math.ens.fr/~bodineau/|Thierry Bodineau]], of the [[http://www.imstat.org/aihp/|Annales de l'Institut Henri Poincaré, Probabilités et Statistique]] From 2006 to 2011, Associate editor of [[http://www.springerlink.com/link.asp?id=100331|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 [[http://www.sciencesmaths-paris.fr/|Fondation Sciences Mathématiques de Paris]] ====== Enseignement ====== Cours "**Rough Paths et EDS**" du master PMA [[https://www.lpsm.paris/masters/modale/index]] Voici le {{BookCGZ.pdf | Poly, tous les chapitres}} (version du 08/04/24) ---- 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 {{csto22.pdf | poly}} Voici le {{TD0.pdf | TD0}} avec des exercices préliminaires et des rappels Voici le {{TD1.pdf | TD1}} Voici le {{TD2.pdf | TD2}} Voici le {{TD3.pdf | TD3}} Voici le {{TD4.pdf | TD4}} Voici le {{TD5.pdf | TD5}} Voici le {{TD6.pdf | TD6}} Voici le {{TD7.pdf | TD7}} Voici des {{annales_calcul_sto.pdf | annales de sujets d'examen}} ====== Research interests ====== * Stochastic (partial) differential equations * Regularity Structures * Rough Paths * Random polymers * Large deviations * Heat conduction models * Neural complexity ====== Publications ====== * Lucas Broux, Francesco Caravenna, Lorenzo Zambotti (2023), [[ https://mc.sbm.org.br/wp-content/uploads/sites/9/sites/9/2023/12/58-Article-1.pdf|An example of singular elliptic stochastic PDE]], Mat. Contemp. 58, 3–67. * Jean-David Jacques, Lorenzo Zambotti (2023), [[https://arxiv.org/abs/2306.02484|Post-Lie algebras of derivations and regularity structures]], arXiv preprint. * Lucas Broux, Francesco Caravenna, Lorenzo Zambotti (2023), [[https://arxiv.org/abs/2301.07517|Hairer's multilevel Schauder estimates without Regularity Structures]], arXiv preprint. * Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia, Lorenzo Zambotti (2023), [[https://arxiv.org/abs/2204.01445|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), [[https://arxiv.org/abs/2110.06928|The Sewing lemma for 0<γ≤1]], J. Funct. Anal. 283, no. 10. * Yvain Bruned, Franck Gabriel, Martin Hairer, Lorenzo Zambotti (2022), [[https://doi.org/10.1090/jams/977|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), [[https://arxiv.org/abs/2009.07640|A Microlocal Approach to Renormalization in Stochastic PDEs]], to appear in [[https://www.worldscientific.com/worldscinet/ccm|Communications in Contemporary Mathematics]], arxiv preprint 2009.07640. * Francesco Caravenna, Lorenzo Zambotti (2020), [[https://arxiv.org/abs/2005.09287|Hairer's Reconstruction Theorem without Regularity Structures]], [[https://ems.press/journals/emss|EMS Surv. Math. Sci.]] 7 (2020), no. 2, 207–251. * K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti (2020), [[https://arxiv.org/abs/2001.03808|Wick polynomials in non-commutative probability]], to appear in [[https://www.cambridge.org/core/journals/canadian-journal-of-mathematics|Canadian J. Math.]], arxiv preprint 2001.03808. * Lorenzo Zambotti (2020), [[https://www.aimsciences.org/article/doi/10.3934/dcds.2020264|A brief and personal history of stochastic partial differential equations]], DCDS. * N. Tapia, L. Zambotti (2020), [[https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12311|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), [[https://link.springer.com/article/10.1007/s00440-019-00926-0|Bessel SPDEs and renormalized local times]], Probab. Theory Related Fields 176, no. 3-4, 757–807. * Yvain Bruned, Martin Hairer, Lorenzo Zambotti (2019), [[https://link.springer.com/article/10.1007/s00222-018-0841-x|Algebraic renormalisation of regularity structures]], Inventiones Mathematicae, Volume 215, Issue 3, pp 1039–1156. * K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti (2018), [[https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rny269/5231876?guestAccessKey=7b18009b-93f9-4a33-93fa-6aa92111e1f4|A Hopf-algebraic approach to cumulants-moments relations and Wick polynomials]], Int. Math. Res. Not. IMRN (2020), no. 24, 10064–10099. * L. Zambotti (2018), [[https://mathscinet.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&review_format=html&s4=zambotti%2C%20l%2A&s5=&s6=&s7=&s8=All&sort=Newest&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=1&mx-pid=3828174|SPDEs and renormalisation]], Stochastic partial differential equations and related fields, 271–277, Springer Proc. Math. Stat., 229, Springer. * Lorenzo Zambotti (2017), [[http://www.springer.com/gp/book/9783319520957|Random Obstacle Problems]], École d'Été de Probabilités de Saint-Flour XLV - 2015, Lecture Notes in Mathematics 2181, Springer. * Mauro Mariani, Lorenzo Zambotti (2016), [[http://arxiv.org/abs/1203.5930|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), [[http://arxiv.org/abs/1111.4388|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), [[http://arxiv.org/abs/1402.3712|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), [[http://link.springer.com/article/10.1007/s40072-014-0026-6|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), [[http://arxiv.org/abs/1105.2779|A skew stochastic heat equation]], Journal of Theoretical Probability: Volume 27, Issue 1, 168-201. * [[http://www.proba.jussieu.fr/~lefevere/rlpage.html|R. Lefevere]], [[http://www.latp.univ-mrs.fr/~mariani/|M. Mariani]], L. Zambotti, (2012)[[http://arxiv.org/abs/1103.2815|Large deviations for a random speed particle]], ALEA Vol. IX, pages 739-760. * [[http://jbuzzi.googlepages.com/|J. Buzzi]], L. Zambotti, (2012) [[http://arxiv.org/abs/0909.2120|Approximate maximizers of intricacy functionals]], Probability Theory and Related Fields, Volume 153, Numbers 3-4, 421-440. * [[http://jbuzzi.googlepages.com/|J. Buzzi]], L. Zambotti, (2012) [[http://www.e-publications.org/ims/submission/index.php/AIHP/user/submissionFile/6778?confirm=dbbf1b9a| 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. * [[http://www.proba.jussieu.fr/~lefevere/rlpage.html|R. Lefevere]], [[http://www.latp.univ-mrs.fr/~mariani/|M. Mariani]], L. Zambotti, (2011) [[http://arxiv.org/abs/1009.2659|Large deviations for renewal processes]], Stochastic Processes and Their Applications, Volume 121, Issue 10, 2243-2271. * [[http://www.proba.jussieu.fr/~lefevere/rlpage.html|R. Lefevere]], [[http://www.latp.univ-mrs.fr/~mariani/|M. Mariani]],L. Zambotti, (2011) [[http://arxiv.org/abs/1007.2664|Large deviations of the current in stochastic collisional dynamics]], J. Math. Phys. 52, no. 3. * [[http://www.proba.jussieu.fr/pageperso/normand/index.htm|R. Normand]], L. Zambotti (2011), [[http://arxiv.org/abs/1002.0702|Uniqueness of post-gelation solutions of a class of coagulation equations]], Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 28, no. 2, 189-215. * [[http://www.proba.jussieu.fr/~lefevere/rlpage.html|R. Lefevere]], [[http://www.latp.univ-mrs.fr/~mariani/|M. Mariani]],L. Zambotti, (2010) [[http://arxiv.org/abs/1007.3080|Macroscopic fluctuations theory of aerogel dynamics]], Journal of Statistical Mechanics, Vol. 2010, Issue 12. * [[http://www.proba.jussieu.fr/~lefevere/rlpage.html|R. Lefevere]],L. Zambotti, (2010) [[http://arxiv.org/abs/0904.0020|Hot scatterers and tracers for the transfer of heat in collisional dynamics]], J. Stat. Phys. Volume 139, 4, Page 686--713. * [[http://www.sns.it/it/scienze/menunews/docentiscienze/ambrosio/|L. Ambrosio]], [[http://www.imati.cnr.it/~savare/|G. Savaré]], L. Zambotti, (2009) [[http://arxiv.org/abs/0704.2458|Existence and Stability for Fokker-Planck equations with log-concave reference measure]], Probability Theory and Related Fields, vol. 145, 517-564. * L. Zambotti, (2008) [[http://arxiv.org/abs/0711.0583|Fluctuations for a conservative interface model on a wall]], ALEA, vol. 4, pp. 167-184. * L. Zambotti, (2008) [[http://arxiv.org/abs/0711.1068|A conservative evolution of the Brownian excursion]], Electronic Journal of Probability, vol. 13, 1096-1119. * [[http://www.math.tu-berlin.de/~mrenesse/|Max-K. Von Renesse]], [[http://www.proba.jussieu.fr/pageperso/yor/|M. Yor]], L. Zambotti, (2008) [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1B-4R8WK37-1&_user=870092&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000046800&_version=1&_urlVersion=0&_userid=870092&md5=9d3bf40e06a5ed34db4a0aec36b4fe14|Quasi-invariance properties of a class of subordinators]], Stochastic Processes and Their Applications, vol. 188 no. 1, 2038-2057. * [[http://www.math.unipd.it/~fcaraven/|F. Caravenna]], [[http://www.proba.jussieu.fr/pageperso/giacomin/GBpage.html|G. Giacomin]], L. Zambotti, (2007) [[http://arXiv.org/abs/math.PR/0604426|Infinite volume limits of polymer chains with periodic charges]],[[http://www.math.msu.su/~malyshev/mprf.htm/| Markov Processes and Related Fields]], vol. 13, no. 4, 697-730. * [[http://www.math.unipd.it/~fcaraven/|F. Caravenna]], [[http://www.proba.jussieu.fr/pageperso/giacomin/GBpage.html|G.Giacomin]], L. Zambotti, (2007) [[http://arXiv.org/abs/math.PR/0507178|A renewal theory approach to periodic copolymers with adsorption]], [[http://imstat.org/aap/|Annals of Applied Probability]], vol. 17, no. 4, 1362-1398. * [[http://www.bretagne.ens-cachan.fr/math/people/arnaud.debussche/|A. Debussche]], L. Zambotti, (2007) [[http://arXiv.org/abs/math.PR/0601313|Conservative Stochastic Cahn-Hilliard equation with reflection]], [[http://www.imstat.org/aop/|Annals of Probability]], vol. 35, no. 5, 1706-1739. * L. Zambotti, (2006) [[http://arXiv.org/abs/math.PR/0603474|Convergence of approximations of monotone gradient systems]], [[http://www.springerlink.com/(qbpfyjqsrqulo145alyciuzz)/app/home/journal.asp?referrer=parent&backto=linkingpublicationresults,1:104879,1|Journal of Evolution Equations]], 6(4), 601-619. * [[http://www.math.unipd.it/~fcaraven/|F. Caravenna]], [[http://www.proba.jussieu.fr/pageperso/giacomin/GBpage.html|G. Giacomin]], L. Zambotti, (2006) [[http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=3540&article=1583&mode=pdf|Sharp asymptotic behavior for wetting models in (1+1)-dimension]], [[http://www.math.washington.edu/~ejpecp/|Electronic Journal of Probability]], 11, 345-362. * [[http://ima.epfl.ch/~rdalang/|Robert C. Dalang]], [[http://www.math.rochester.edu/people/faculty/cmlr/|Carl Mueller]], L. Zambotti, (2006) [[http://arxiv.org/abs/math.PR/0410414|Hitting properties of parabolic s.p.d.e.'s with reflection]]. [[http://www.imstat.org/aop/|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 [[http://search.tandf.co.uk/bookscatalogue.asp?URL=https://ecommerce.tandf.co.uk/catalogue/DirectLink.asp?ResourceCentre=SEARCH&ContinentSelected=0&CountrySelected=0&USSelected=0&ChangeCountry=0&search_text=0824700279&SearchGroup=ISBN&results_order=ByTitle&querytext=stochastic%20partial&database=Books|Stochastic Partial Differential Equations and Applications - VII]], edited by [[http://www.sns.it/it/scienze/menunews/docentiscienze/daprato/|G. Da Prato]] and [[http://www.science.unitn.it/~tubaro/|L. Tubaro]], pp. 337-347, Taylor & Francis Group. * [[http://www.math.tu-berlin.de/stoch/HOMEPAGES/deuschel.html|J.-D. Deuschel]], [[http://www.proba.jussieu.fr/pageperso/giacomin/GBpage.html|G. Giacomin]], L. Zambotti, (2005) [[http://www.springerlink.com/(phjg5m45ovcqtbq1eevq5lqt)/app/home/contribution.asp?referrer=parent&backto=issue,1,4;journal,10,528;linkingpublicationresults,1:100451,1| Scaling limits of equilibrium wetting models in (1+1)-dimension]]. [[http://www.springerlink.com/openurl.asp?genre=journal&issn=0178-8051|Prob. Theory and Rel. Fields]], 132 n. 4, 471 - 500. * L. Zambotti, (2005) [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJJ-4DTBT4C-1&_coverDate=06%2F01%2F2005&_alid=317685195&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6880&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=2330ef61a1e89655f69bfa6fa1c48fb4|Integration by parts on the law of the reflecting Brownian motion]]. [[http://www.elsevier.com/wps/find/journaldescription.cws_home/622879/description|J. Funct. Anal.]], 223 n. 1, 147-178. * [[http://www.math.tu-berlin.de/stoch/HOMEPAGES/deuschel.html|J.-D. Deuschel]], L. Zambotti, (2005) [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1B-4FG4SNX-1&_coverDate=06%2F30%2F2005&_alid=317686704&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5670&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=721f76874bcbbb57063d34e1bdb2ecf0|Bismut-Elworthy's formula and random walk representation for SDEs with reflection]]. [[http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5670&_auth=y&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=6d62b8645224f2c7674fdfcbe5dee115| Stochastic Process. Appl.]], 115 n. 6, pp 907-925. * [[http://www.proba.jussieu.fr/pageperso/yor.html|M. Yor]], L. Zambotti (2004) [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1D-4CDJ7NS-1&_coverDate=07%2F01%2F2004&_alid=317687843&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5672&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=5e44113761d4a6ac3a4f055e06ef442d|A Remark About the Norm of a Brownian Bridge]], [[http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5672&_auth=y&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=379ab76f4c0058625ea174233e3f1835| Statist. Probab. Lett.]], 68 n. 3, 297--304. * L. Zambotti, (2004) [[http://www.springerlink.com/(phjg5m45ovcqtbq1eevq5lqt)/app/home/contribution.asp?referrer=parent&backto=issue,1,6;journal,23,528;linkingpublicationresults,1:100451,1|Fluctuations for a \nabla\varphi interface model with repulsion from a wall]], [[http://www.springerlink.com/(phjg5m45ovcqtbq1eevq5lqt)/app/home/contribution.asp?referrer=parent&backto=issue,1,6;journal,23,528;linkingpublicationresults,1:100451,1|Prob. Theory and Rel. Fields]], 129 n. 3, 315-339. * L. Zambotti, (2004) [[http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.aop/1078415833|Occupation densities for SPDEs with reflection]], [[http://www.imstat.org/aop/|Annals of Probability]], 32 n. 1A, 191-215. * [[http://alpha.science.unitn.it/~bonaccor/|S. Bonaccorsi]], L. Zambotti, (2004) [[http://www.ams.org/journal-getitem?pii=S0002993903070977|Integration by parts on the Brownian Meander]], [[http://www.ams.org/proc/|Proc. Amer. Math. Soc.]], 132 n. 3, 875-883. * L. Zambotti, (2003) [[http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.aop/1046294313|Integration by parts on \delta-Bessel Bridges, \delta > 3, and related SPDEs]], [[http://www.imstat.org/aop/|Annals of Probability]], 31 n. 1, 323-348. * L. Zambotti, (2002) [[http://www.springerlink.com/(sm3ovp45dwvd0o45w0axby45)/app/home/contribution.asp?referrer=parent&backto=issue,5,6;journal,46,528;linkingpublicationresults,1:100451,1|Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection]], [[http://www.springerlink.com/openurl.asp?genre=journal&issn=0178-8051|Probab. Theory Related Fields]], 123 n. 4, 579--600. * L. Zambotti, (2002) [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X1B-453X5RF-7&_coverDate=02%2F01%2F2002&_alid=317699589&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=7238&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=c8aa93fe6d42f5bfb4a4dce5f09c5538|Integration by parts on Bessel Bridges and related Stochastic PartialDifferential Equations]], [[http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=7238&_auth=y&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=5f10a7a6eac8fcb6b462bffb91dd50f2|C. R. Acad. Sci. Paris]], Ser. I, 334 n. 3, 209-212. * L. Zambotti, (2001) [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJJ-457D558-46&_coverDate=02%2F20%2F2001&_alid=317700870&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6880&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=86a9600fbeb9b519d837713e221e374d|A reflected stochastic heat equation as symmetric dynamics with respect to the 3-d Bessel bridge]], [[http://www.elsevier.com/wps/find/journaldescription.cws_home/622879/description|J. Funct. Anal.]], 180 n. 1, 195--209. * L. Zambotti, (2000) [[http://www.springerlink.com/(phjg5m45ovcqtbq1eevq5lqt)/app/home/contribution.asp?referrer=parent&backto=issue,1,5;journal,68,528;linkingpublicationresults,1:100451,1|An analytic approach to existence and uniqueness for martingale problems in infinite dimensions]], [[http://www.springerlink.com/openurl.asp?genre=journal&issn=0178-8051|Probab. Theory Related Fields]], 118 n. 2, 147--168. * [[http://www2.dm.unito.it/paginepersonali/priola/|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.