Hoeffding’s inequality and convex ordering
dominicyeo
[Ho63] addresses the alternative model where the increments of a random walk are chosen uniformly without replacement from a particular set. The potted summary is that the sum of random increments chosen without replacement has the same mean, but is more concentrated that the corresponding sum of random increments chosen with replacement. This means that any of the concentration results proved in the earlier sections of [Ho63] for the latter situation apply equally to the setting without replace