2024/06/04 by Marek Biskup, Biskup, Marek, Stephan Gufler +3
Mathematics · Physics and Astronomy · #28A78 #60G15 #60G57 #60G60 #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2406.02814
openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study fractal properties of support sets of the critical Liouville Quantum Gravity (cLQG) associated with the Gaussian Free Field in planar domains. Specifically, we completely characterize the gauge functions ϕ (subject to mild monotonicity conditions) for which the cLQG admits a support set of finite ϕ-Hausdorff measure. As a corollary, we settle the conjecture that the cLQG is supported on a set of vanishing Hausdorff dimension. Our proofs are based on the fact that the cLQG describes the near-critical level sets of Discrete Gaussian Free Field.