5 citations · 14 across the 30 of their papers we have counts for
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Geodesic networks in Liouville quantum gravity surfaces
Ewain Gwynne
Recent work has shown that for , a Liouville quantum gravity (LQG) surface can be endowed with a canonical metric. We prove several results concerning geodesics for thi…
Geodesics and metric ball boundaries in Liouville quantum gravity
Ewain Gwynne, Joshua Pfeffer, Scott Sheffield
Recent works have shown that there is a canonical way to to assign a metric (distance function) to a Liouville quantum gravity (LQG) surface for any parameter . We esta…
Tightness of supercritical Liouville first passage percolation
Jian Ding, Ewain Gwynne
Liouville first passage percolation (LFPP) with parameter is the family of random distance functions on the plane obtained by integrating along p…
The distance exponent for Liouville first passage percolation is positive
Jian Ding, Ewain Gwynne, Avelio Sepúlveda
Discrete Liouville first passage percolation (LFPP) with parameter is the random metric on a sub-graph of obtained by assigning each vertex a weight of $e^…
Random walks on mated-CRT planar maps and Liouville Brownian motion
Nathanael Berestycki, Ewain Gwynne
We prove a scaling limit result for random walk on certain random planar maps with its natural time parametrization. In particular, we show that for , the random walk o…