Large deviations of the Schwarzian field theory
Abstract
We prove a large deviations principle for the probabilistic Schwarzian Field Theory at low temperatures. We demonstrate that the good rate function is equal to the action of the Schwarzian Field Theory, and we find its minimisers. In addition, we define an analogue of the Hölder condition on the functional space Diff1(T)/PSL(2,R) in terms of cross-ratio observables, characterise them in terms of the usual Hölder property on the space of continuous functions, and deduce the corresponding compact embedding theorem. We also show that the Schwarzian measure concentrates on functions satisfying the defined condition.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Analytic and geometric function theory
Black Holes and Theoretical Physics
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 3
- Publication date
- 21 April 2026
- Language
- EN