  Previous models have shown that stochastic scattering of stars in a
two-dimensional galaxy disc can generate a time-independent surface density
distribution that is an exponential divided by radius when a constant inward
scattering bias is present. Here we show, using a Markov chain model, that
similar profiles result from an outward scattering bias, although the disc
surface density decreases slowly with time because of a net stellar outflow.
The trend towards a near-exponential surface profile is robust, as it exists
even if the scattering intensity has moderate radial and time dependences,
subject to some limitations on the scattering rates discussed in the text. The
exponential scale length of the pseudo-equilibrium disc depends on the
scattering bias, the scattering length, and the size of the disc where
scattering is important.
