Positive harmonic functions on biregular trees

Source abstract

We show that if $f$ is a positive harmonic function on a biregular tree which has maximal growth along an infinite path in the tree, then every harmonic function $g$ on the tree with $0\leq g\leq f$ is a multiple of $f$, thus generalizing a result of Cartier about regular trees. Received: 28 April 2023 | Accepted: 9 August 2023