Primordial non-Gaussianities and zero bias tracers of the Large Scale
  Structure
  We develop a new method to constraint primordial non-Gaussianities of the
local kind using unclustered tracers of the Large Scale Structure. We show that
in the limit of low noise, zero bias tracers yield large improvement over
standard methods, mostly due to vanishing sampling variance. We propose a
simple technique to construct such a tracer, using environmental information
obtained from the original sample, and validate our method with N-body
simulations. Our results indicate that
$\sigma_{f_{\mathrm{NL}}^{\mathrm{loc}}}\simeq1$ can be reached using only
information on a single tracer of sufficiently high number density.
