Open Access
2020 Large deviations of radial SLE$_{\infty }$
Morris Ang, Minjae Park, Yilin Wang
Electron. J. Probab. 25: 1-13 (2020). DOI: 10.1214/20-EJP502


We derive the large deviation principle for radial Schramm-Loewner evolution ($\operatorname {SLE}$) on the unit disk with parameter $\kappa \rightarrow \infty $. Restricting to the time interval $[0,1]$, the good rate function is finite only on a certain family of Loewner chains driven by absolutely continuous probability measures $\{\phi _{t}^{2} (\zeta )\, d\zeta \}_{t \in [0,1]}$ on the unit circle and equals $\int _{0}^{1} \int _{S^{1}} |\phi _{t}'|^{2}/2\,d\zeta \,dt$. Our proof relies on the large deviation principle for the long-time average of the Brownian occupation measure by Donsker and Varadhan.


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Morris Ang. Minjae Park. Yilin Wang. "Large deviations of radial SLE$_{\infty }$." Electron. J. Probab. 25 1 - 13, 2020.


Received: 19 February 2020; Accepted: 26 July 2020; Published: 2020
First available in Project Euclid: 28 August 2020

Digital Object Identifier: 10.1214/20-EJP502

Primary: 60F10 , 60J67

Keywords: Brownian occupation measure , large deviations , Loewner-Kufarev equation , Schramm-Loewner Evolutions

Vol.25 • 2020
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