  We investigate the origin of halo assembly bias, the dependence of halo
clustering on assembly history. We relate halo assembly to peak properties
measured in the Lagrangian space of the initial linear Gaussian random density
field, and show how these same Lagrangian properties determine large-scale
bias. We focus on the two regimes where assembly bias has been observed to be
significant: at masses very large and very small compared to the nonlinear mass
scale. At high masses, we show that assembly bias is expected from the
statistics of the peaks of Gaussian random fluctuations, and we show that the
extent of assembly bias found in N-body simulations of rare halos is in
excellent agreement with our theoretical prediction. At low masses, we argue
that assembly bias largely arises from a sub-population of low mass halos whose
mass accretion has ceased. Due to their arrested development, these halos
naturally become unbiased, in contrast to their anti-biased peers. We show that
a simple toy model incorporating these effects can roughly reproduce the bias
trends found in N-body simulations.
