For dynamical percolation in Z^d, the paper derives the e^{-2λ} term in the speed expansion and proves that on the critical curve μ²=p(1-p), d≥2, the speed is eventually increasing in the bias.
Directed diffusion in a percolation network.Journal of Physics C: Solid State Physics, 16(8):1451, 1983
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Biased random walk on the critical curve of dynamical percolation
For dynamical percolation in Z^d, the paper derives the e^{-2λ} term in the speed expansion and proves that on the critical curve μ²=p(1-p), d≥2, the speed is eventually increasing in the bias.