2020/01/01 by Morris Ang, Minjae Park, Yilin Wang · 2 citations
Mathematics · #Absolute continuity #Brownian motion #Interval (graph theory) #Large deviations theory #Mathematical Dynamics and Fractals #Measure (data warehouse) #Probability measure #Random Matrices and Applications #Rate function #Stochastic processes and statistical mechanics #Unit circle #Unit interval #math.CV #math.PR
paper · pdf · doi:10.1214/20-ejp502
published in Electronic Journal of Probability 25(none) (Institute of Mathematical Statistics) · 17 pages, 1 figure, revised according to referee's report
openalex publication_date 2020/01/01 · openalex created_date 2020/02/14 · arxiv created 2020/07/31 · arxiv updated 2020/08/31 · openalex updated_date 2026/08/06
We derive the large deviation principle for radial Schramm-Loewner evolution (\operatorname SLE) on the unit disk with parameter κ → ∞ . 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 \φ t2 (ζ ) dζ \t ∈ [0,1] on the unit circle and equals ∫ 01 ∫ S1 |φ t'|2/2 dζ dt. Our proof relies on the large deviation principle for the long-time average of the Brownian occupation measure by Donsker and Varadhan.