  We study the asymptotic behavior of the eigenvalue distribution of the
Baxter's corner transfer matrix (CTM) and the density matrix (DM) in the
White's density-matrix renormalization group (DMRG), for one-dimensional
quantum and two-dimensional classical statistical systems. We utilize the
relationship ${\rm DM}={\rm CTM}^4$ which holds for non-critical systems in the
thermodynamic limit. Using the known diagonal form of CTM, we derive exact
asymptotic form of the DM eigenvalue distribution for the integrable $S=1/2$
XXZ chain (and its related integrable models) in the massive regime. The result
is then recast into a ``universal'' form without model-specific quantities,
which leads to $\omega_{m}\sim \exp[-{\rm const.}(\log m)^2]$ for $m$-th DM
eigenvalue at larg $m$. We perform numerical renormalization group calculations
(using the corner-transfer-matrix RG and the product-wavefunction RG) for
non-integrable models, verifying the ``universal asymptotic form'' for them.
Our results strongly suggest the universality of the asymptotic eigenvalue
distribution of DM and CTM for a wide class of systems.
