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Numerical simulation of the two-dimensional bond percolation at the percolation threshold on an L*L lattice shows that the radius of gyration of singly connected bonds (SCB) scales as L1. This result confirms an assumption used to derive a lower bound on the critical exponent of elasticity. A persistent anisotropy in the distribution of SCB is found and used to estimate the ratio between the bulk and shear moduli of a random percolating system. Local anisotropy in the direction of SCB disappears for large L.
Yacov Kantor (Sun,) studied this question.