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Multiple tracers of the same surveyed volume can enhance the signal-to-noiseon a measurement of local primordial non-Gaussianity and the relativisticprojections. Increasing the number of tracers comparably increases the numberof shot noise terms required to describe the stochasticity of the data.Although the shot noise is white on large scales, it is desirable toinvestigate the extent to which it can degrade constraints on the parameters ofinterest. In a multi-tracer analysis of the power spectrum, a marginalizationover shot noise does not degrade the constraints on $f_\text{NL}$ by more than$\sim 30$% so long as halos of mass $M\lesssim 10^{12}M_\odot$ are resolved.However, ignoring cross shot noise terms induces large systematics on ameasurement of $f_\text{NL}$ at redshift $z<1$ when small mass halos areresolved. These effects are less severe for the relativistic projections,especially for the dipole term. In the case of a low and high mass tracer, theoptimal sample division maximizes the signal-to-noise on $f_\text{NL}$ and theprojection effects simultaneously, reducing the errors to the level of $\sim10$ consecutive mass bins of equal number density. We also emphasize that thenon-Poissonian noise corrections that arise from small-scale clustering effectscannot be measured with random dilutions of the data. Therefore, they musteither be properly modeled or marginalized over.

Shot noise in multi-tracer constraints on $f_\text{NL}$ and relativistic projections: Power Spectrum