KPZ relation does not hold for the level lines and the SLE_κ flow lines of the Gaussian free field [article]

Juhan Aru
2014 arXiv   pre-print
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_κ 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
more » ... d to pass nearby a fixed point. This extends previous results on winding of SLE curves by Schramm.
arXiv:1312.1324v2 fatcat:oglko4zhkvgf5ifauxcrykvr6m