  We present a matrix model which is intended as a toy model of the gauge dual
of an AdS black hole. In particular, it captures the key property that at
infinite $N$ correlators decay to zero on long time scales, while at finite $N$
this cannot happen. The model consists of a harmonic oscillator in the adjoint
which acts as a heat bath for a particle in the fundamental representation. The
Schwinger-Dyson equation reduces to a closed recursion relation, which we study
by various analytical and numerical methods. We discuss some implications for
the information problem.
