Avelio Sepúlveda (ETH Zurich)

Based on joint work with Juhan Aru, Titus Lupu and Wendelin Werner. Two-dimensional continuum Gaussian free field (GFF) has been one of the main objects of conformal invariant probability theory in the last ten years. The GFF is the two-dimensional analogue of Brownian motion when the time set is replaced by a 2-dimensional domain. Although one can not make sense of the GFF as a proper function, it can be seen as a «generalized function» (i.e. a Schwartz distribution). The main objective of this talk is to go through recent development in the understanding of the analogue, in the GFF context, of Ito’s excursion theory for Brownian motion. As a corollary, we will see how this theory can be used to define the Lévy transform of the GFF.