Institut de Physique Théorique
Direction de la Recherche Fondamentale  -  Saclay
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Vendredi 22 septembre 2017

Publication : t17/147

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Integral means spectrum of whole-plane SLE

Beliaev D. ()
Duplantier B. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Zinsmeister M. ()
Abstract:
We complete the mathematical analysis of the fine structure of harmonic measure on SLE curves that was initiated by Beliaev and Smirnov, as described by the averaged integral means spectrum. For the unbounded version of whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and Loutsenko and Yermolayeva, a phase transition has been shown to occur for high enough moments from the bulk spectrum towards a novel spectrum related to the point at infinity. For the bounded version of whole-plane SLE studied here, a similar transition phenomenon, now associated with the SLE origin, is proved to exist for low enough moments, but we show that it is superseded by the earlier occurrence of the transition to the SLE tip spectrum.
Année de publication : 2017
Revue : Commun. Math. Phys. 353 119-133 (2017)
DOI : 10.1007/s00220-017-2868-z
Preprint : arXiv:1605.03112
Keywords : Mathematical Physics; Complex Variables
Langue : Anglais

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