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Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the way distinct ...
Brownian motion correlation in the peanosphere for κ >8
(ElsevierAnnales de l'institut Henri Poincare (B) Probability and Statistics, 2017-11-01)
The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$-Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent ...