Liouville Quantum Duality and Random Planar Maps

2025/07/16 by Bertrand Duplantier, Duplantier, Bertrand, Emmanuel Guitter +1
Mathematics · #Markov Chains and Monte Carlo Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2507.12203

Abstract

We consider models of block-weighted random planar maps in which possibly decorated maps are decomposed canonically into blocks, each block receiving the weight u. These maps present a transition at some critical value u=u_cr above which the maps degenerate into Brownian trees. We show that the enumerative properties and critical exponents of the maps at u=u_cr and those for u

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