Thick points of the GFF and CLE nesting fieldsOberseminar Stochastics

Thursday Jul 3, 2025, 4:30 PM → 5:30 PM Europe/Berlin

Endenicher Allee 60/0-011 - Seminarraum (Mathezentrum)

“Thick points” of the GFF are points where, roughly speaking, the field is atyp-
ically high. They provide insight into the geometric properties of the field,
and are the basis for the construction of so-called Liouville (quantum gravity)
measures. The set of thick points with thickness level a is a fractal set with
Hausdorff dimension $2 − a^2/2$. In this talk I will discuss another fundamental
property, namely, that the set is almost surely disconnected for all non-zero
a. This is based on joint work with Juhan Aru and Léonie Papon, and uses a
remarkable relationship between the GFF and the conformal loop ensemble
of parameter 4.