A distance exponent for Liouville quantum gravity

@article{Gwynne2016ADE,
  title={A distance exponent for Liouville quantum gravity},
  author={Ewain Gwynne and Nina Holden and Xin Sun},
  journal={Probability Theory and Related Fields},
  year={2016},
  volume={173},
  pages={931-997}
}
Let $$\gamma \in (0,2)$$γ∈(0,2) and let h be the random distribution on $$\mathbb C$$C which describes a $$\gamma $$γ-Liouville quantum gravity (LQG) cone. Also let $$\kappa = 16/\gamma ^2 >4$$κ=16/γ2>4 and let $$\eta $$η be a whole-plane space-filling SLE$$_\kappa $$κ curve sampled independent from h and parametrized by $$\gamma $$γ-quantum mass with respect to h. We study a family $$\{\mathcal G^\epsilon \}_{\epsilon >0}$${Gϵ}ϵ>0 of planar maps associated with $$(h, \eta )$$(h,η) called the… 
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