# Bounds for distances and geodesic dimension in Liouville first passage percolation

@article{Gwynne2019BoundsFD,
title={Bounds for distances and geodesic dimension in Liouville first passage percolation},
author={Ewain Gwynne and Joshua Pfeffer},
journal={Electronic Communications in Probability},
year={2019}
}
• Published 1 January 2019
• Mathematics
• Electronic Communications in Probability
For $\xi \geq 0$, Liouville first passage percolation (LFPP) is the random metric on $\varepsilon \mathbb Z^2$ obtained by weighting each vertex by $\varepsilon e^{\xi h_\varepsilon(z)}$, where $h_\varepsilon(z)$ is the average of the whole-plane Gaussian free field $h$ over the circle $\partial B_\varepsilon(z)$. Ding and Gwynne (2018) showed that for $\gamma \in (0,2)$, LFPP with parameter $\xi = \gamma/d_\gamma$ is related to $\gamma$-Liouville quantum gravity (LQG), where $d_\gamma$ is the…
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Discrete and continuum Liouville first passage percolation (DLFPP, LFPP) are two approximations of the conjectural $\gamma$-Liouville quantum gravity (LQG) metric, obtained by exponentiating the