100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Thierry Gallay

Depuis lundi 18 mai, le bâtiment de l'Institut Fourier est à nouveau accessible par badge ou code, de 6h30 à 18h30, du lundi au vendredi (hors jours fériés et pont de l'Ascension). Les locaux communs, dont la cafétéria et la bibliothèque, restent fermés jusqu'à nouvel ordre. Un registre de présence devant être tenu, les membres du laboratoire souhaitant accéder à leur bureau sont priés de s'annoncer en répondant aux sondages envoyés par la direction du laboratoire. Le travail à distance doit toutefois rester la règle autant que possible. Pour de plus amples informations, consulter l'intranet du laboratoire.

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Planar Gaussian fields are a model of spatial noise, and in many applications it is useful to understand the geometric structure of their level sets. There is a natural classification of geometric functionals of the level sets as either local' (e.g. length of the level sets, volume of the excursion sets, Euler characteristic of the excursion sets) or 'non-local' (e.g. number of components of the level/excursion sets, percolation of the level/excursion sets) depending on whether there exists an integral representation for the functional. In the case of local' functionals, first order properties (e.g. asymptotics for the mean) are easily derived from the Kac-Rice formula, and second order properties (e.g. asymptotics for the variance, central limit theorems) can also be established via Weiner chaos expansions (Kratz--Leon '11, Estrade--Leon '16, Marinucci--Rossi--Wigman '17, Nourdin--Peccati--Rossi '17 etc). For the non-local' number of level/excursion sets the analysis is more challenging, and while first order properties were established 10 years ago by Nazarov--Sodin using ergodic theoretical techniques, up until now there have been essentially no second order results. In this talk I will discuss some first steps in this directions, namely proving lower bounds on the variance which are of correct' order. Joint work with Dmitry Belyaev and Michael McAuley (University of Oxford).