  We apply the multi-tracer technique to test the possibility of improved
constraints on the amplitude of local primordial non-Gaussianity,
$f_{\mathrm{NL}}$, in the cosmic large-scale structure. A precise measurement
of $f_{\mathrm{NL}}$ is difficult because the effects of non-Gaussianity mostly
arise on the largest scales, which are heavily affected by the low statistical
sampling commonly referred to as cosmic variance. The multi-tracer approach
suppresses cosmic variance and we implement it by combining the information
from next-generation galaxy surveys in the optical/near-infrared band and
neutral hydrogen (HI) intensity mapping surveys in the radio band.
High-redshift surveys enhance the precision on $f_{\mathrm{NL}}$, due to the
larger available volume, and HI intensity mapping surveys can naturally reach
high redshifts. In order to extend the redshift coverage of a galaxy survey, we
consider different emission-line galaxy populations, focusing on the H$\alpha$
line at low redshift and on oxygen lines at higher redshift. By doing so, we
cover a wide redshift range $1 \lesssim z \lesssim 4$. To assess the capability
of our approach, we implement a synthetic-data analysis by means of Markov
chain Monte Carlo sampling of the (cosmological+nuisance) parameter posterior,
to evaluate the constraints on $f_{\mathrm{NL}}$ obtained in different survey
configurations. We find significant improvements from the multi-tracer
technique: the full data set leads to a precision of $\sigma(f_{\mathrm{NL}}) <
1$.
