Large deviations of Schramm-Loewner evolutions: A survey

Abstract

These notes survey the first results on large deviations of Schramm-Loewner evolutions (SLE) with emphasis on interrelations between rate functions and applications to complex analysis. More precisely, we describe the large deviations of SLE${}_{\kappa }$ when the $\kappa$ parameter goes to zero in the chordal and multichordal case and to infinity in the radial case. The rate functions, namely Loewner and Loewner-Kufarev energies, are closely related to the Weil-Petersson class of quasicircles and real rational functions.

52 pages, 3 figures, revised according to referee's report. To appear in Probability surveys

References in corpus (4)

• Duality of Chordal SLE
• A Sharp Condition for the Loewner Equation to Generate Slits
• Reversibility of chordal SLE
• Exact Solutions for Loewner Evolutions

Cited by in corpus (4)

• The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles
• Refined regularity of SLE
• Two-loop Loewner potentials
• A deterministic approach to Loewner-energy minimizers