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One of the main signatures of primordial non-Gaussianity of the local type isa scale-dependent correction to the bias of large-scale structure tracers suchas galaxies or clusters, whose amplitude depends on the bias of the tracersitself. The dominant source of noise in the power spectrum of the tracers iscaused by sampling variance on large scales (where the non-Gaussian signal isstrongest) and shot noise arising from their discrete nature. Recent work hasargued that one can avoid sampling variance by comparing multiple tracers ofdifferent bias, and suppress shot noise by optimally weighting halos ofdifferent mass. Here we combine these ideas and investigate how well thesignatures of non-Gaussian fluctuations in the primordial potential can beextracted from the two-point correlations of halos and dark matter. On thebasis of large $N$-body simulations with local non-Gaussian initial conditionsand their halo catalogs we perform a Fisher matrix analysis of the two-pointstatistics. Compared to the standard analysis, optimal weighting- andmultiple-tracer techniques applied to halos can yield up to one order ofmagnitude improvements in $\fnl$-constraints, even if the underlying darkmatter density field is not known. We compare our numerical results to the halomodel and find satisfactory agreement. Forecasting the optimal$\fnl$-constraints that can be achieved with our methods when applied toexisting and future survey data, we find that a survey of$50h^{-1}\mathrm{Gpc}^3$ volume resolving all halos down to $10^{11}\hMsun$ at$z=1$ will be able to obtain $\sigma_{\fnl}\sim1$ (68% cl), a factor of$\sim20$ improvement over the current limits. Decreasing the minimum mass ofresolved halos, increasing the survey volume or obtaining the dark matter mapscan further improve these limits, potentially reaching the level of$\sigma_{\fnl}\sim0.1$. (abridged)

Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure