On asymptotic variance of whole-plane SLE

Ho, Xuan Hieu; Le, Thanh Binh

doi:10.1090/proc/14124

On asymptotic variance of whole-plane SLE
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by Xuan Hieu Ho and Thanh Binh Le

Proc. Amer. Math. Soc. 146 (2018), 5181-5193

DOI: https://doi.org/10.1090/proc/14124

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 $\mathrm {SLE}_{2}$. 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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