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On asymptotic variance of whole-plane SLE

Authors: Xuan Hieu Ho and Thanh Binh Le
Journal: Proc. Amer. Math. Soc. 146 (2018), 5181-5193
MSC (2010): Primary 30C99; Secondary 30C62
Published electronically: September 10, 2018
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Abstract: In this paper we rigorously compute the average McMullen asymptotic variance for the logarithmic derivative of the interior whole-plane Schramm-Loewner evolution $ \textup {SLE}_{2}$. Combined with some earlier results on the integral mean spectrum by B. Duplantier, Chi T. P. Nguyen, Nga T. T. Nguyen, and M. Zinsmeister (see also B.Duplantier, Hieu X. Ho, Binh T. Le, and M. Zinsmeister (2015 and 2017)), we prove an analogue of McMullen dimension formula.

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Xuan Hieu Ho
Affiliation: Bâtiment de Mathématiques MAPMO, UFR Sciences, Université d’Orléans, rue de Chartres, B.P.6759, Orleans Cedex 2 45067, France

Thanh Binh Le
Affiliation: Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong Street, Quy Nhon, Binh Dinh, Vietnam

Received by editor(s): November 14, 2017
Received by editor(s) in revised form: January 30, 2018
Published electronically: September 10, 2018
Dedicated: Dedicated to Professor Michel Zinsmeister on the occasion of his $60$th birthday
Communicated by: Jeremy T. Tyson
Article copyright: © Copyright 2018 American Mathematical Society

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