This seminar will be presented in hybrid mode. The speaker will deliver his talk in person.
Title: Percolation for two-dimensional excursions clouds and the Gaussian free field
Abstract: We study the excursion process, a random soup of Markov chains which can be interpreted as a two-dimensional version of random interlacements, both in the discrete and continuous setting. Using SLE theory, the critical parameters associated to the percolation of the corresponding vacant sets can be identified. I will also present bounds on the critical parameter associated to the percolation of the level sets of the two-dimensional discrete Gaussian free field with Dirichlet boundary conditions. This leads to a set of inequalities between these critical parameters in dimension two, which were either known or conjectured only in higher dimension.
The talk will be followed by refreshments in the Huxley Common Room at 4pm.