On the infinite differentiability of the right edge in the supercritical oriented percolation

Consider the oriented percolation model. Let r n be the right edge. By a subadditive argument, it is known that lim n → ∞ r n n = α ( p ) a . s . and in L 1 . In this paper, we show α ( p ) is infinitely differentiable in p for all 1 > p > p c .