TY - JOUR

T1 - Integral Means Spectrum of Whole-Plane SLE

AU - Beliaev, Dmitry

AU - Duplantier, Bertrand

AU - Zinsmeister, Michel

N1 - Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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phenomenon, now associated with the SLE origin, is proved to exist for low enough moments, but we show that it is superseded by the earlier occurrence of the transition to the SLE tip spectrum.

AB - 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phenomenon, now associated with the SLE origin, is proved to exist for low enough moments, but we show that it is superseded by the earlier occurrence of the transition to the SLE tip spectrum.

UR - http://www.scopus.com/inward/record.url?scp=85017184894&partnerID=8YFLogxK

U2 - 10.1007/s00220-017-2868-z

DO - 10.1007/s00220-017-2868-z

M3 - Article

AN - SCOPUS:85017184894

VL - 353

SP - 119

EP - 133

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -