7 April 2017
Communications in Mathematical Physics
We complete the mathematical analysis of the fine structure of harmonic measure on SLE curves that was initiated in Beliaev and Smirnov (Commun Math Phys 290(2):577–595, 2009), as described by the averaged integral means spectrum. For the unbounded version of whole-plane SLE as studied in Duplantier et al. (Ann Henri Poincaré 16(6):1311–1395, 2014. arXiv:1211.2451) and Loutsenko and Yermolayeva (J Stat Mech P04007, 2013), 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 of Beliaev and Smirnov, 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phenomenon, now associated with the SLE origin, is proved to exist for low enough moments, but we show that it is superseded by the earlier occurrence of the transition to the SLE tip spectrum.
Submitted to ORA: