Liouville metric of star-scale invariant fields: tails and Weyl scaling

2018/09/07 by Julien Dubédat, Dubédat, Julien, Hugo Falconet +1 · 1 citation
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1809.02607

openalex publication_date 2018/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter γ_c >0, the left-right length of rectangles for the Riemannian metric e^γϕ_0,n ds² with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when γ< min ( γ_c, 0.4) and that subsequential limits are consistent with the Weyl scaling.

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