  In the Master's thesis of the author, we investigate certain aspects of
gravitational physics that emerge from stochastic toy models of holographic
gauge theories. We begin by reviewing field theory thermodynamics, black hole
thermodynamics and how the AdS / CFT correspondence provides a link between the
two. We then study a nonlinear evolution equation for the energy density that
was derived last year from a random walk governed by the density of states.
When one dimension is non-compact, a variety of field theories produce long
lived plasma balls that are dual to black holes. This is due to a trapping
phenomenon associated with the Hagedorn density of states. With the help of
numerical and mathematical results, we show that problems arise when two or
more dimensions are non-compact. A natural extension of our model involves a
system of partial differential equations for both energy and momentum. Our
second model is shown to have some desired, but also some undesired properties,
such as a potential disagreement with hydrodynamics.
