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Generalized Multifractality of Whole-Plane SLE

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If you have a question about this talk, please contact Mustapha Amrani.

Random Geometry

Co-authors: H Ho (Orlans University), B Le (Orlans University), M Zinsmeister (Orlans 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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