On the topological pressure of axial product on trees

This paper investigates the topological pressure of isotropic axial products of Markov subshifts on the [Formula: see text]-tree. We show that the quantity increases with dimension [Formula: see text]. To achieve this, we introduce the pattern distribution vectors and the associated transition matrices and partially transplant the large deviation theory to tree-shifts. Additionally, we apply our main result to a broader class of shift spaces, accompanied by numerical experiments for verification.