Characterization of the threshold for multi-range percolation on oriented trees

Abstract

We give a characterization of the percolation threshold for a multirange model on oriented trees, as the first positive root of a polynomial, with the use of a multi-type Galton-Watson process. This gives in particular the exact value of the critical point for the model studied in [2] and [3] for k = 2.

arXiv commentThis preprint has been incorporated into arXiv:2510.03922