Volume of metric balls in Liouville quantum gravity

@article{Ang2020VolumeOM,
  title={Volume of metric balls in Liouville quantum gravity},
  author={Morris Ang and Hugo Falconet and Xin Sun},
  journal={arXiv: Probability},
  year={2020}
}
We study the volume of metric balls in Liouville quantum gravity (LQG). For $\gamma \in (0,2)$, it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG volume of Euclidean balls has finite moments exactly for $p \in (-\infty, 4/\gamma^2)$. Here, we prove that the LQG volume of LQG metric balls admits all finite moments. This answers a question of Gwynne and Miller and generalizes a result obtained by Le Gall for the Brownian map, namely, the $\gamma = \sqrt{8/3… 

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