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We calculate the eigenvalues of a class of random matrices, namely therandomly segmented tridiagonal quasi-Toeplitz (rstq-T) matrix, in exactclosed-form. The contexts under which these matrices arise are ubiquitous inphysics. In our case, they arise when studying the dynamics of a Rouse polymerembedded in random environments. Unlike in the case of Rouse polymers inhomogeneous environments, where the dynamics give rise to a circulant matrixand the diagonalization is achieved easily via a Fourier transform, analyticaldiagonalization of the rstq-T matrix has remained unsolved thus far. Weanalytically calculate the spectral distribution of the rstq-T matrix, which isable to capture the effect of disorder on the modes.

Closed form Eigenvalues of Randomly Segmented Tridiagonal quasi-Toeplitz Matrices: Random Rouse block copolymer