Correction Growth Profile and Invariant Measures for the Weakly Supercritical Contact Process on a Homogeneous Tree By

The proof of Theorem 3 in [1] is incorrect, as it relies on a faulty use of the strong Markov property. The theorem asserts that β = β(λ) is strictly increasing in λ for λ < λ2, where λ is the infection rate parameter for the contact process, λ2 is the upper critical value (at the transition from weak to strong survival), and β = limn→∞ u n where un = probability that a vertex xn at distance n from the root is ever infected, given that only the root is infected at time t = 0. In this note we shall prove the following slightly weaker result.