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In this lecture series some important objects of random geometry are introduced and studied. In particular, the relation between the Gaussian free field and random walks / Brownian motions is explored
We construct a measure on the thick points of a Brownian loop soup in a bounded domain DD of the plane with given intensity theta>0θ>0, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...
WILEY2023
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In a previous article, we introduced the first passage set (FPS) of constant level -aof the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the bo ...
Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining ...