  We study a class of noncommutative gauge theory models on 2-dimensional Moyal
space from the viewpoint of matrix models and explore some related properties.
Expanding the action around symmetric vacua generates non local matrix models
with polynomial interaction terms. For a particular vacuum, we can invert the
kinetic operator which is related to a Jacobi operator. The resulting
propagator can be expressed in terms of Chebyschev polynomials of second kind.
We show that non vanishing correlations exist at large separations. General
considerations on the kinetic operators stemming from the other class of
symmetric vacua, indicates that only one class of symmetric vacua should lead
to fast decaying propagators. The quantum stability of the vacuum is briefly
discussed.
