2016/01/21 by Gábor Pete, Hao Wu, Pete, Gábor +1 · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1601.05713
openalex publication_date 2016/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct an aggregation process of chordal SLE(κ) excursions in the unit disk, starting from the boundary, growing towards all inner points simultaneously, invariant under all conformal self-maps of the disk. We prove that this conformal growth process of excursions, abbreviated as CGE(κ), exists iff κ∈ [0,4), and that it does not create additional fractalness: the Hausdorff dimension of the closure of all the SLE(κ) arcs attached is 1+κ/8 almost surely. We determine the dimension of points that are approached by CGE(κ) at an atypical rate, and construct conformally invariant random fields on the disk based on CGE(κ).