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.
MR 2884873 13, 111 [SSW09] O
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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.