Speaker
Prof.
Duplantier Bertrand
Summary
We introduce a generalized notion of integral means spectrum for
unbounded conformal maps, depending on two moments, giving access to
logarithmic coefficients. We study this (averaged) generalized integral
means spectrum for unbounded whole-plane SLE. The usual SLE multifractal
spectrum, predicted by the speaker in 2000 and proved in expectation
by Beliaev and Smirnov in 2005 and almost surely by Gwynne, Miller and Sun
in 2014, crosses over to a novel spectrum along phase transition lines in
the plane of moment orders. A conjecture is also proposed for the
universal generalized multifractal spectrum, which is proved for a
certain range of moments.
