  We discuss the relationship between the large order behavior of the
perturbative series for the average plaquette in pure gauge theory and
singularities in the complex coupling plane. We discuss simple extrapolations
of the large order for this series. We point out that when these extrapolated
series are subtracted from the Monte Carlo data, one obtains (naive) estimates
of the gluon condensate that are significantly larger than values commonly used
in the continuum for phenomelogical purpose. We present numerical results
concerning the zeros of the partition function in the complex coupling plane
(Fisher's zeros). We report recent attempts to solve this problem using the
density of states. We show that weak and strong coupling expansions for the
density of states agree surprisingly well for values of the action relevant for
the crossover regime.
