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Generalized Multifractality of Whole-Plane SLE

Wednesday 28th January 2015 - 15:00 to 16:00
INI Seminar Room 1
Co-authors: H Ho (Orléans University), B Le (Orléans University), M Zinsmeister (Orléans University)

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 (average) generalized integral means spectrum for unbounded whole-plane SLE. The usual SLE multifractal spectrum, predicted by the author in 2000 and proved by Beliaev and Smirnov in 2005 and 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 proposed for the universal generalized multifractal spectrum, which is proved for a certain range of moments.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons