The mapping p to sigma(p) for supercritical bond percolation on Z^d is C^infinity on (p_c,1], a full-interval extension of Kozlov's 1989 result.
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The diffusivity of supercritical Bernoulli percolation is infinitely differentiable
The mapping p to sigma(p) for supercritical bond percolation on Z^d is C^infinity on (p_c,1], a full-interval extension of Kozlov's 1989 result.