## 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

## Abstract:

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.## References

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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: xuan-hieu.ho@univ-orleans.fr
**Thanh Binh Le**- Affiliation: Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong Street, Quy Nhon, Binh Dinh, Vietnam
- Email: mr.lethanhbinh@gmail.com
- Received by editor(s): November 14, 2017
- Received by editor(s) in revised form: January 30, 2018
- Published electronically: September 10, 2018
- 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: https://doi.org/10.1090/proc/14124
- MathSciNet review: 3866857

Dedicated: Dedicated to Professor Michel Zinsmeister on the occasion of his $60$th birthday