Geodesic
A large deviation principle for the Schramm–Loewner evolution in the uniform topology
Vladislav Guskov1
1KTH Royal Institute of Technology, Department of Mathematics
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 389-410

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We establish a large deviation principle for chordal SLE$_\kappa$ parametrized by capacity, as the parameter $\kappa \to 0+$, in the topology generated by uniform convergence on compact intervals of the positive real line. The rate function is shown to equal the Loewner energy of the curve. This strengthens the recent result of Peltola and Wang who obtained the analogous statement using the Hausdorff topology.
DOI : 10.54330/afm.130997
Keywords: Schramm–Loewner evolution, large deviation principle, Loewner energy

Vladislav Guskov  1

1 KTH Royal Institute of Technology, Department of Mathematics 
Vladislav Guskov. A large deviation principle for the Schramm–Loewner evolution in the uniform topology. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 389-410. doi: 10.54330/afm.130997
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