A characteristic feature of black holes is that they are able to trap energy/information for a long time before releasing it. In this talk, we consider the question of how this trapping arises in the holographic field theory models that provide nonperturbative definitions of quantum gravitational physics. Using a simple stochastic toy model, we find evidence that the Hagedorn densities of states that are often associated with large N gauged matrix degrees of freedom (and/or with the existence of strings in the dual theory) may play a significant role in the energy trapping.