Conditional block-size laws and multifractal spectra in block-weighted planar maps match exactly those of Liouville quantum gravity with added atomic measures, with a universal partition-function ratio and one model-specific constant per realization.
Distance statistics in quadrangulations with no multiple edges and the geometry of minbus.Journal of Physics A: Mathe- matical and Theoretical, 43(20):205207, apr 2010
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Liouville Quantum Duality and Random Planar Maps II
Conditional block-size laws and multifractal spectra in block-weighted planar maps match exactly those of Liouville quantum gravity with added atomic measures, with a universal partition-function ratio and one model-specific constant per realization.