On the Equivalence of Barrier Crossing, Peak-Background Split, and Local Biasing

Several, apparently distinct, formalisms exist in the literature for predicting the clustering of dark matter halos. It has been noticed on a case-by-case basis that the predictions of these different methods agree in specific examples, but there is no general proof that they are equivalent. In this paper, we give a simple proof of the mathematical equivalence of barrier crossing, peak-background split, and local biasing.