2016/01/04 by K. J. Falconer, Falconer, Kenneth, Xiong Jin +1 · 2 citations
Mathematics · #28A80 #60D05 #81T40 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1601.00556
openalex publication_date 2016/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a measure ν on a regular planar domain D, the Gaussian multiplicative chaos measure of ν studied in this paper is the random measure \widetilde ν obtained as the limit of the exponential of the γ-parameter circle averages of the Gaussian free field on D weighted by ν. We investigate the dimensional and geometric properties of these random measures. We first show that if ν is a finite Borel measure on D with exact dimension α>0, then the associated GMC measure \widetilde ν is non-degenerate and is almost surely exact dimensional with dimension α-(γ2)/(2), provided (γ2)/(2)