  We study diffusion on a substrate with permanent traps distributed with
critical positional correlation, modeled by their placement on the perimeters
of a critical percolation cluster. We perform a numerical analysis of the
vibrational density of states and the largest eigenvalue of the equivalent
scalar elasticity problem using the method of Arnoldi and Saad. We show that
the critical trap correlation increases the exponent appearing in the stretched
exponential behavior of the low frequency density of states by approximately a
factor of two as compared to the case of no correlations. A finite size scaling
hypothesis of the largest eigenvalue is proposed and its relation to the
density of states is given. The numerical analysis of this scaling postulate
leads to the estimation of the stretch exponent in good agreement with the
density of states result.
