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KPZ relation does not hold for the level lines and the SLE$_κ$ flow lines of the Gaussian free field

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 conditioned to pass nearby a fixed point. This extends previous results on winding of SLE curves by Schramm.

preprint2014arXivOpen access
Juhan Aru
math-phmath.PRmath.MP
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Juhan Aru

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