  We consider the maximum of the discrete two dimensional Gaussian free field
in a box, and prove the existence of a (dense) deterministic subsequence along
which the maximum, centered at its mean, is tight; this still leaves open the
conjecture that tightness holds without the need for subsequences. The method
of proof relies on an argument developed by Dekking and Host for branching
random walks with bounded increments and on comparison results specific to
Gaussian fields.
