  We study the statistical and dynamic properties of the systems characterized
by an ultrametric space of states and translationary non-invariant symmetric
transition matrices of the Parisi type subjected to "locally constant"
randomization. Using the explicit expression for eigenvalues of such matrices,
we compute the spectral density for the Gaussian distribution of matrix
elements. We also compute the averaged "survival probability" (SP) having sense
of the probability to find a system in the initial state by time $t$. Using the
similarity between the averaged SP for locally constant randomized Parisi
matrices and the partition function of directed polymers on disordered trees,
we show that for times $t>t_{\rm cr}$ (where $t_{\rm cr}$ is some critical
time) a "lacunary" structure of the ultrametric space occurs with the
probability $1-{\rm const}/t$. This means that the escape from some bounded
areas of the ultrametric space of states is locked and the kinetics is confined
in these areas for infinitely long time.
