FPP distance in random quadrangulations and planar maps scales asymptotically as a constant times graph distance; Tutte bijection preserves this equivalence at large scales.
Scaling limits of random trees and planar maps
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First-passage percolation in random planar maps and Tutte's bijection
FPP distance in random quadrangulations and planar maps scales asymptotically as a constant times graph distance; Tutte bijection preserves this equivalence at large scales.