An introduction to the MalliavinStein method
A hacking day of Mathematics for Data Science at the Department of Mathematics

Bio
Ph.D. Thesis in Mathematics, December 2002. Université Paris VI September 2003September 2008. Maître de Conférences, LSTA, Paris VI Habilitation à Diriger des recherches, December 2006, LSTA, Paris V September 2008January 2010: Professeur des Universités (Full Professor), Modal'X, Université Paris Ouest. February 2010Now: Full Professor, Université du Luxembourg. Head of the Department of Mathematics of Luxembourg University since 2018. Elected IMS Fellow 2018.Syllabus
I will present the basic features of the socalled MalliavinStein method, consisting of a fruitful combination of Malliavin calculus and of Stein’s method for probabilistic approximations. Originally introduced in 2007 by Ivan Nourdin and the speaker, such a collection of techniques has gained enormous relevance in the last 10 years, in particular for its application to stochastic geometry (random graphs, and geometry of random fields). I will discuss several applications: to fourthmoment theorems on a Gaussian space, to the highfrequency analysis of random waves and to the derivation of functional inequalities and concentration estimates.
References
 Nourdin, Ivan; Peccati, Giovanni. Normal approximations with Malliavin calculus. From Stein’s method to universality. Cambridge Tracts in Mathematics, 192. Cambridge University Press, Cambridge, 2012
 Nourdin, Ivan; Peccati, Giovanni; Rossi, Maurizia. Nodal statistics of planar random waves. Comm. Math. Phys. 369 (2019), no. 1, 99151
 Ledoux, Michel; Nourdin, Ivan; Peccati, Giovanni. Stein’s method, logarithmic Sobolev and transport inequalities. Geom. Funct. Anal. 25 (2015), no. 1, 256306.
Schedule
 Thursday 15 October 2020 @ 15.0018.00
 Friday 16 October 2020 @ 15.0018.00
Details
 Participation is free, however a notification by email to Prof. Claudio Agostinelli is mandatory
 For further information, please contact Prof. Claudio Agostinelli
 Venue: Webinar, credentials will be sent to the participants the day before of the event
 Language: English