<span style="color: #000000;">Recently, by introducing the notion of cumulatively merged partition, M<span style="color: #800000;">énard<span style="color: #000000;"> and Singh provide <span style="color: #000000;">a sufficient condition on graphs ensuring that the critical value of the contact process is positive. In this note, we show that the one-dimensional long range percolation with high exponent satisfies their condition and thus the contact process exhibits a non-trivial phase transition.
"Contact process on one-dimensional long range percolation." Electron. Commun. Probab. 20 1 - 11, 2015. https://doi.org/10.1214/ECP.v20-4461