  In this paper, we consider the time averaged distribution of discrete time
quantum walks on the glued trees. In order to analyse the walks on the glued
trees, we consider a reduction to the walks on path graphs. Using a spectral
analysis of the Jacobi matrices defined by the corresponding random walks on
the path graphs, we have spectral decomposition of the time evolution operator
of the quantum walks. We find significant contributions of the eigenvalues $\pm
1$ of the Jacobi matrices to the time averaged limit distribution of the
quantum walks. As a consequence we obtain lower bounds of the time averaged
distribution.
