  In recent work (Seljak, Hamaus and Desjacques 2009) it was found that
weighting central halo galaxies by halo mass can significantly suppress their
stochasticity relative to the dark matter, well below the Poisson model
expectation. In this paper we extend this study with the goal of finding the
optimal mass-dependent halo weighting and use $N$-body simulations to perform a
general analysis of halo stochasticity and its dependence on halo mass. We
investigate the stochasticity matrix, defined as $C_{ij}\equiv<(\delta_i
-b_i\delta_m)(\delta_j-b_j\delta_m)>$, where $\delta_m$ is the dark matter
overdensity in Fourier space, $\delta_i$ the halo overdensity of the $i$-th
halo mass bin and $b_i$ the halo bias. In contrast to the Poisson model
predictions we detect nonvanishing correlations between different mass bins. We
also find the diagonal terms to be sub-Poissonian for the highest-mass halos.
The diagonalization of this matrix results in one large and one low eigenvalue,
with the remaining eigenvalues close to the Poisson prediction $1/\bar{n}$,
where $\bar{n}$ is the mean halo number density. The eigenmode with the lowest
eigenvalue contains most of the information and the corresponding eigenvector
provides an optimal weighting function to minimize the stochasticity between
halos and dark matter. We find this optimal weighting function to match linear
mass weighting at high masses, while at the low-mass end the weights approach a
constant whose value depends on the low-mass cut in the halo mass function.
Finally, we employ the halo model to derive the stochasticity matrix and the
scale-dependent bias from an analytical perspective. It is remarkably
successful in reproducing our numerical results and predicts that the
stochasticity between halos and the dark matter can be reduced further when
going to halo masses lower than we can resolve in current simulations.
