  We analyze the dynamics of a random sequential message passing algorithm for
approximate inference with large Gaussian latent variable models in a
student-teacher scenario. To model nontrivial dependencies between the latent
variables, we assume random covariance matrices drawn from rotation invariant
ensembles. Moreover, we consider a model mismatching setting, where the teacher
model and the one used by the student may be different. By means of dynamical
functional approach, we obtain exact dynamical mean-field equations
characterizing the dynamics of the inference algorithm. We also derive a range
of model parameters for which the sequential algorithm does not converge. The
boundary of this parameter range coincides with the de Almeida Thouless (AT)
stability condition of the replica symmetric ansatz for the static
probabilistic model.
