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Central limit theorems for random walks in quenched random environments haveattracted plenty of attention in the past years. More recently still, finerlocal limit theorems -- yielding a Gaussian density multiplied by a highlyoscillatory modulating factor -- for such models have been obtained. In theone-dimensional nearest-neighbor case with i.i.d. transition probabilities,local limits of uniformly elliptic ballistic walks are now well understood. Wecomplete 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 proofis, out of necessity, entirely different from the ballistic case.

A local limit theorem for random walks in balanced environments