%0 Journal Article %T Substitutions and 1/2-Discrepancy of $\{n ¦È+ x\}$ \rm{II} %A David Ralston %J Mathematics %D 2011 %I arXiv %X Ergodic properties of a renormalization procedure for studying the 1/2-discrepancy sums driven by rotations are studied, with corresponding implications for almost-sure bounds on the growth rates for these discrepancy sums. %U http://arxiv.org/abs/1105.6301v1