Liouville Quantum Gravity on the unit disk

2015/02/15 by Yichao Huang, Rémi Rhodes, Huang, Yichao +3 · 7 citations
Mathematics · Physics and Astronomy · #30F10 #60D05 #81T20 #81T40 #Differential Geometry (math.DG) #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 #math-ph #math.DG #math.MP #math.PR #msc:30F10 #msc:60D05 #msc:81T20 #msc:81T40

paper · pdf · doi:10.48550/arxiv.1502.04343

openalex publication_date 2015/02/15 · arxiv created 2017/07/17 · arxiv updated 2017/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains with boundary. We also make precise conjectures about the relationship of this theory to scaling limits of random planar maps with boundary conformally embedded onto the disk.

Citations

• Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula

Cited by

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• Bulk/boundary quotients of Gaussian multiplicative chaos measures II: Tail profile of bulk Gaussian multiplicative chaos measures in the exact scale-invariant case
• Probabilistic construction of non compactified imaginary Liouville field theory

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