Thierry LÉVY

Professor of mathematics
Université Pierre et Marie Curie (Paris 6)
Laboratoire de Probabilités et Modèles aléatoires

Email : Prénom.Nom@upmc.fr
Office : 15-16 2 19
Phone : +33 1 44 27 80 04

Address :

LPMA, UMR 7599 Université Paris 6 - Case courrier 188 4 place Jussieu 75252 Paris Cedex 05 (FRANCE)

Teaching

• Probabilités et statistiques (L3, module LM345),
• Probabilités de base (M1, module MM010).

Research subjects

• Two-dimensional Yang-Mills measure
• Markovian random holonomy fields
• Large N limit of the Yang-Mills field, master field
• Heat kernel on compact Lie groups
• Free probability
• Quantum deformations of the Yang-Mills measure

Coauthors

Prepublications

• Asymptotics of Brownian motions on classical Lie groups, the master field on the plane, and the Makeenko-Migdal equations. [arXiv:1112.2452].
• Prefixes of minimal factorisations of a cycle. [arXiv:1105.5763].

Published papers

• Topological quantum field theories and Markovian Random fields. Bull. Sci. Math. 135 (2011), no. 6-7, 629--649.
• A continuous semigroup of notions of independence between the classical and the free one. Ann. Prob. 39 (2011), 3, 904--938. [arXiv:0811.2335], with Florent Benaych-Georges.
• Central limit theorem for the heat kernel measure on the unitary group. J. Funct. Anal. 259 (2010), 12, 3163--3204. [arXiv:0905.3282], with Mylène Maïda.
  
• Two-dimensional Markovian holonomy fields. Astérisque, 329 (2010). [arXiv:0804.2230]
• Schur-Weyl duality and the heat kernel measure on the unitary group. Adv. Math. 218 (2008), 2, 537--575. [math/0703690]
• Discrete and continuous Yang-Mills measure for non-trivial bundles over compact surfaces.  Probab. Theory Related Fields 136 (2006), 2, 171--202. [math-ph/0501014]
• Large deviations for the Yang-Mills measure on a compact surface.  Comm. Math. Phys. 261 (2006), 2, 405--450. [math-ph/0406027] , with James R. Norris.
• Wilson loops in the light of spin networks. J. Geom. Phys. 52 (2004), 4, 382--397. [math-ph/0306059]
  
• Yang-Mills measure on compact surfaces.  Mem. Amer. Math. Soc. 166 (2003),790, xiv+122 pp. [math.PR/0101239]
• Construction et étude à l'échelle microscopique de la mesure de Yang-Mills sur les surfaces compactes. C. R. Math. Acad. Sci. Paris 330 (2000), 11.

Survey articles

• Large deviations for the two-dimensional Yang-Mills measure, Proceedings of the conference "Stochastic Analysis in Mathematical Physics" (Lisbonne 2006). [World Scientific]
• Comment choisir une connexion au hasard? [How to choose a connection at random ?] Séminaire de Théorie Spectrale et Géométrie. Vol. 21. Année 2002--2003, 61--73. [Download]

Lecture notes

• Differential equations driven by rough paths, Lecture Notes in Mathematics Vol. 1908. Lectures of Terry J. Lyons at the 2004 Saint-Flour Summer school. (written in collaboration with Michael J. Caruana). Consulter les errata.
• Probabilistic methods in statistical physics. Lecture notes of a course given at Tsinghua University (Beijin) in Octobre 2008.