[[index|Cette page en français]] ==== Thierry Lévy ==== Professor at the [[https://www.lpsm.paris/|LPSM]] (Laboratoire de Probabilités, Statistique et Modélisation), at [[https://www.sorbonne-universite.fr/|Sorbonne Université]]\\ Member of the [[https://www.lpsm.paris/recherche/les-equipes/httpswwwlpsmparisrechercheles-equipesdynamique-probabilites-geometrie/|Dynamics, probability, geometry]] team\\ Mail : \\ Postal address : Sorbonne Université, LPSM -- 4, place Jussieu -- F-75005 Paris\\ Office : 16-26 120 ---- === Teaching === In Master 1 : [[probas approfondies|Probabilités approfondies]] -- UE MU4MA011\\ In Master 2 : [[CGP|Convergence de mesures, Grandes déviations, Percolation]] (CGP) I am deputy director of the [[http://master.math.sorbonne-universite.fr/fr/niveau_m1.html|Master of mathematics]], in charge of the M1. ---- === Research === == Research topics == My work is related, more or less directly, to the probabilistic study of gauge theories, on a two-dimensional Euclidean space-time or on graphs. I have studied the Yang-Mills measure on surfaces, its semi-classical limit, its "large N" limit. In the last few years, I have been interested in the geometry and statistical physics of graphs with a vector bundle and a connection. In my work, I use parts of the differential geometry of principal bundles, the representation theory of classical compact Lie groups and symmetric groups, the theory of large random matrices, non-commutative probability, in particular free probability, the theory of determinantal point processes. I have occasionally used potential theory in the complex plane and large deviations. Among the things I have not yet worked with, I am particularly interested in Chern--Simons theory and the Wess--Zumino--Witten model, quantum deformations of the Yang--Mills measure, the theory of regularity structures. == Prepublications == * On the mean projection theorem for determinantal point processes, avec [[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]. [ [[https://arxiv.org/abs/2203.04628|arXiv:2203.04628]] ] == Publications == * Determinantal probability measures on Grassmannians. To appear in [[https://www.ems-ph.org/journals/forthcoming.php?jrn=aihpd|Ann. Inst. Henri Poincaré D]], avec [[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]. [ [[https://arxiv.org/abs/1910.06312|arXiv:1910.06312]] ] * Covariant Symanzik identities. [[https://msp.org/pmp/2021/2-3/p01.xhtml|Probability and Mathematical Physics]], **2** (2021) no. 3, 419–475, avec [[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]. * Two-dimensional quantum Yang--Mills theory and the Makeenko--Migdal equations. [[https://www.springer.com/gp/book/9783030564087"|Frontiers in analysis and probability]], 275--325, Springer (2020). [ [[https://arxiv.org/abs/1912.06246|arXiv:1912.06246]] ] * A colourful path to matrix-tree theorems. [[https://alco.centre-mersenne.org/item/ALCO_2020__3_2_471_0/|Algebraic Combinatorics]], **3** (2020), no. 2, 471--482 , avec [[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]. [ [[http://arxiv.org/abs/1903.02491|arXiv:1903.02491]] ] * Four chapters on low-dimensional gauge theories. [[https://www.springer.com/gp/book/9783319634524|Stochastic geometric mechanics]], Springer Proc. Math. Stat. **202** (2017), 115--167, avec [[https://ambarnsg.wordpress.com/about/|Ambar N. Sengupta]]. * The master field on the plane. [[http://smf.emath.fr/Publications/Asterisque/|Astérisque]], **388** (2017). [ [[http://arxiv.org/abs/1112.2452|arXiv:1112.2452]] ] * The number of prefixes of minimal factorisations of a cycle. [[http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i3p35|Electron. J. Combin]], **23** (2016) no. 3. * On The Douglas--Kazakov phase transition. [[http://www.esaim-proc.org/articles/proc/abs/2015/04/proc145106/proc145106.html|ESAIM: Proc.]], **51** (2015), avec [[http://math.univ-lille1.fr/~maida/|Mylène Maïda]]. * Topological quantum field theories and Markovian random fields. [[href="http://www.sciencedirect.com/science/article/pii/S0007449711000790|Bull. Sci. Math.]], **135** (2011) no. 6-7, 629--649. * A continuous semigroup of notions of independence between the classical and the free one. [[http://www.imstat.org/aop/|Ann. Prob.]], **39** (2011) no. 3, 904--938, avec [[http://www.cmapx.polytechnique.fr/%7Ebenaych/|Florent Benaych-Georges]]. [ [[http://hal.archives-ouvertes.fr/hal-00338778/fr/|arXiv:0811.2335]] ] * Central limit theorem for the heat kernel measure on the unitary group. [[http://www.sciencedirect.com/science/article/pii/S0022123610003150|J. Funct. Anal]], **259** (2010) no. 12, 3163--3204, avec [[http://math.univ-lille1.fr/~maida/|Mylène Maïda]]. [ [[http://arxiv.org/abs/0905.3282|arXiv:0905.3282]] ] * Two-dimensional Markovian holonomy fields. [[http://smf.emath.fr/Publications/Asterisque/|Astérisque]], **329** (2010). [ [[http://arxiv.org/abs/0804.2230|arXiv:0804.2230]] ] * Schur--Weyl duality and the heat kernel measure on the unitary group. [[http://www.sciencedirect.com/science/journal/00018708|Adv. Math.]], **218** (2008) no. 2, 537--575. [ [[https://arxiv.org/abs/math/0703690|arXiv:math/0703690]] ] * Differential equations driven by rough paths, [[http://www.springer.com/math/probability/book/978-3-540-71284-8|Lecture Notes in Mathematics]] Vol. 1908. Notes du cours de [[https://www.maths.ox.ac.uk/people/terry.lyons|Terry J. Lyons]] à l'école d'été de [[http://math.univ-bpclermont.fr/stflour/|Saint-Flour]] en 2004. Rédigées avec [[https://www.cancercouncil.com.au/research/research-we-conduct/our-researchers/dr-michael-caruana/|Michael J. Caruana]]. * Large deviations for the two-dimensional Yang--Mills measure, Actes de la conférence [[http://gfm.cii.fc.ul.pt/events/samp2006/|Stochastic Analysis in Mathematical Physics]] (Lisbonne 2006). [[http://www.worldscibooks.com/mathematics/6734.html|World Scientific]]. * Discrete and continuous Yang--Mills measure for non-trivial bundles over compact surfaces. [[http://www.springerlink.com/content/1432-2064/|Probab. Theory Related Fields]], **136** (2006) no. 2, 171--202. [ [[https://arxiv.org/abs/math-ph/0501014|arXiv:math-ph/0501014]] ] * Large deviations for the Yang--Mills measure on a compact surface. [[http://www.springerlink.com/content/1432-0916/|Comm. Math. Phys.]], **261** (2006) no. 2, 405--450, avec [[http://www.statslab.cam.ac.uk/Dept/People/norris.html|James R. Norris]]. [ [[https://arxiv.org/abs/math-ph/0406027|arXiv:math-ph/0406027]] ] * Wilson loops in the light of spin networks. [[http://www.sciencedirect.com/science/journal/03930440|J. Geom. Phys.]], **52** (2004) no. 4, 382--397. [ [[https://arxiv.org/abs/math-ph/0306059|arXiv:math-ph/0306059]] ] * Yang--Mills measure on compact surfaces. [[http://www.ams.org/journals/memo/|Mem. Amer. Math. Soc.]], **166** (2003) no. 790, xiv+122 pp. [ [[https://arxiv.org/abs/math/0101239|arXiv:math/0101239]] ] * Comment choisir une connexion au hasard ? [[http://www-fourier.ujf-grenoble.fr/-Actes-TSG-.html|Séminaire de Théorie Spectrale et Géométrie]] Vol. **21** (2002--2003), 61--73. [[http://archive.numdam.org/ARCHIVE/TSG/TSG_2002-2003__21_/TSG_2002-2003__21__61_0/TSG_2002-2003__21__61_0.pdf|Accès au texte]]. * Construction et étude à l'échelle microscopique de la mesure de Yang--Mills sur les surfaces compactes. [[http://www.academie-sciences.fr/publications/comptes_rendus/CR_mathematique.htm|C. R. Math. Acad. Sci. Paris]], **330** (2000) no. 11. == Coauthors == * [[http://www.cmapx.polytechnique.fr/%7Ebenaych/|Florent Benaych-Georges]] * [[https://www.cancercouncil.com.au/research/research-we-conduct/our-researchers/dr-michael-caruana/|Michael J. Caruana]] * [[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]] * [[https://www.maths.ox.ac.uk/people/terry.lyons|Terry J. Lyons]] * [[http://math.univ-lille1.fr/~maida/|Mylène Maïda]] * [[http://www.statslab.cam.ac.uk/%7Ejames/|James R. Norris]] * [[https://ambarnsg.wordpress.com/about/|Ambar N. Sengupta]] ----