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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On asymptotic variance of whole-plane SLE
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by Xuan Hieu Ho and Thanh Binh Le PDF
Proc. Amer. Math. Soc. 146 (2018), 5181-5193 Request permission


In this paper we rigorously compute the average McMullen asymptotic variance for the logarithmic derivative of the interior whole-plane Schramm–Loewner evolution $\mathrm {SLE}_{2}$. 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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Additional Information
  • Xuan Hieu Ho
  • Affiliation: Bâtiment de Mathématiques MAPMO, UFR Sciences, Université d’Orléans, rue de Chartres, B.P.6759, Orleans Cedex 2 45067, France
  • Email:
  • Thanh Binh Le
  • Affiliation: Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong Street, Quy Nhon, Binh Dinh, Vietnam
  • Email:
  • 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
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 5181-5193
  • MSC (2010): Primary 30C99; Secondary 30C62
  • DOI:
  • MathSciNet review: 3866857