  Central limit theorems for random walks in quenched random environments have
attracted plenty of attention in the past years. More recently still, finer
local limit theorems -- yielding a Gaussian density multiplied by a highly
oscillatory modulating factor -- for such models have been obtained. In the
one-dimensional nearest-neighbor case with i.i.d. transition probabilities,
local limits of uniformly elliptic ballistic walks are now well understood. We
complete the picture by proving a similar result for the only recurrent case,
namely the balanced one, in which such a walk is diffusive. The method of proof
is, out of necessity, entirely different from the ballistic case.
