Random walks on critical site percolation clusters converge to CLE6 Brownian motion and intrinsic metrics converge to CLE6 geodesics, implying existence of chemical distance, resistance, and spectral dimension exponents that satisfy Einstein relations.
Kumagai.Random walks on disordered media and their scaling limits, volume 2101 ofLecture Notes in Mathematics
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The scaling limit of random walk and the intrinsic metric on planar critical percolation
Random walks on critical site percolation clusters converge to CLE6 Brownian motion and intrinsic metrics converge to CLE6 geodesics, implying existence of chemical distance, resistance, and spectral dimension exponents that satisfy Einstein relations.