Abstract:Liouville first passage percolation (LFPP) with parameter ξ > 0 is the family of random distance functions {D h } >0 on the plane obtained by integrating e ξh along paths, where {h } >0 is a smooth mollification of the planar Gaussian free field. Recent works have shown that for all ξ > 0 the LFPP metrics, appropriately re-scaled, admit non-trivial subsequential limiting metrics. In the case when ξ < ξ crit ≈ 0.41, it has been shown that the subsequential limit is unique and defines a metric on γ-Liouville qua… Show more
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