Corrigendum to: The contact process on periodic trees

Abstract

In [1] we considered periodic trees in which the number of children in successive generations is $(n,a_1,\dots ,a_k)$ with ${max}_i{a}_i\le C{n}^{1-\mathit{\delta }}$ and $(log{a}_i)∕logn\to b_i$ as $n\to \mathrm{\infty }$. Our proof contained an error. In this note we correct the proof. The theorem has changed: the critical value for local survival is asymptotically $\sqrt{{\overline{c}}_k(logn)∕n}$ where $l_k=max\{i:0\le i\le k,a_i\ne 1\}$ and ${\overline{c}}_k=min\{k+1-l_k-b_{l_k},(k-b)∕2\}$, where $b={lim}_{n\to \mathrm{\infty }}log(a_1{a}_2\cdots a_k)∕logn$.