  We will investigate a random mass splitting model and the closely related
random walk in a random environment (RWRE). The heat kernel for the RWRE at
time t is the mass splitting distribution at t. We prove a quenched invariance
principle for the RWRE which gives us a quenched central limit theorem for the
mass splitting model. Our RWRE has an environment which is changing with time.
We follow the outline for proving a quenched invariant process for a random
walk in a space-time random environment laid out by Rassoul-Agha and
Sepp\"al\"ainen which in turn was based on the work of Kipnis and Varadhan and
others.
