# Weak LQG metrics and Liouville first passage percolation

@article{Dubedat2020WeakLM,
title={Weak LQG metrics and Liouville first passage percolation},
author={Julien Dub'edat and Hugo Falconet and Ewain Gwynne and Joshua Pfeffer and Xin Sun},
journal={Probability Theory and Related Fields},
year={2020},
pages={1-68}
}
• Published 1 May 2019
• Mathematics
• Probability Theory and Related Fields
For $$\gamma \in (0,2)$$ γ ∈ ( 0 , 2 ) , we define a weak $$\gamma$$ γ - Liouville quantum gravity ( LQG ) metric to be a function $$h\mapsto D_h$$ h ↦ D h which takes in an instance of the planar Gaussian free field and outputs a metric on the plane satisfying a certain list of natural axioms. We show that these axioms are satisfied for any subsequential limits of Liouville first passage percolation. Such subsequential limits were proven to exist by Ding et al. (Tightness of Liouville first…
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There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge $${{\mathbf {c}}}_{\mathrm M} \in (-\infty ,1]$$ c M ∈ ( -