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In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution and the KPZ relation in a natural way, shedding new light on all of them. Our principal result shows that the level lines and the SLE$_\kappa$ flow lines of the Gaussian free field do not satisfy the usual KPZ relation. In order to prove this, we have to make a technical detour: by a careful study of a certain diffusion process, we provide exact estimates of the exponential moments of winding of chordal SLE curves conditioned to pass nearby a fixed point. This extends previous results on winding of SLE curves by Schramm.

Author

Aru, Juhan

Published

2013

Language

EN