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Liouville first passage percolation (LFPP) with parameter $\xi > 0$ is the family of random distance functions $\{D_h^\epsilon\}_{\epsilon >0}$ on the plane obtained by integrating $e^{\xi h_\epsilon}$ along paths, where $\{h_\epsilon\}_{\epsilon >0}$ is a smooth mollification of the planar Gaussian free field.
Liouville quantum gravity with matter central charge in (1, 25): a probabilistic approach
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Bounds for distances and geodesic dimension in Liouville first passage percolation
E. Gwynne and J. Pfeffer · 1903
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Comparison of discrete and continuum Liouville first passage percolation
M. Ang · 1904
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Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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Weak LQG metrics and Liouville first passage percolation
J. Dubédat, H. Falconet, E. Gwynne, J. Pfeffer, and X. Sun · 1905
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Confluence of geodesics in Liouville quantum gravity for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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J. Ding and E. Gwynne · 2005
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Introduction to the Gaussian Free Field and Liouville Quantum Gravity
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