  Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level
system interacting with a $n\times n$ reservoir and assuming that the
interaction is modelled by a random matrix. We presented there a formula for
the reduced density matrix in the limit $n\to \infty $ as well as several its
properties and asymptotic forms in various regimes. In this paper we give the
proofs of the assertions, and present also a new fact about the model.
