Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any degree of precision, improving a result of Zlatoš [Andrej Zlatoš, Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal. 207 (2004) 216–252].