Brownian loop soup and Liouville measure

VIENNA PROBABILITY SEMINAR

On the one hand, 2D Gaussian free field (GFF) is a log-correlated Gaussian field whose exponential defines a random measure: the so-called Liouville measure. On the other hand, critical Brownian loop soup is an infinite collection of loops whose occupation field is distributed like half of the GFF squared (Le Jan's isomorphism). The purpose of this talk is to understand the infinitesimal contribution of one loop to Liouville measure in the above coupling. Based on a joint work with É. Aïdékon, N. Berestycki and T. Lupu.