  Using a numerical simulation of the classical dynamics of the plane-wave and
flat space matrix models of M-theory, we study the thermalization, equilibrium
thermodynamics and fluctuations of these models as we vary the temperature and
the size of the matrices, N. We present our numerical implementation in detail
and several checks of its precision and consistency. We show evidence for
thermalization by matching the time-averaged distributions of the matrix
eigenvalues to the distributions of the appropriate Traceless Gaussian Unitary
Ensemble of random matrices. We study the autocorrelations and power spectra
for various fluctuating observables and observe evidence of the expected
chaotic dynamics as well as a hydrodynamic type limit at large N, including
near-equilibrium dissipation processes. These configurations are
holographically dual to black holes in the dual string theory or M-theory and
we discuss how our results could be related to the corresponding supergravity
black hole solutions.
