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A general feature of particle transport in the core of tokamak plasmas is that when core particle sources are small, a stationary peaked density profile is provided by a balance of outward diffusion and inward convection, driven by either neoclassical or turbulent mechanisms. The turbulent contribution to the off-diagonal elements of the transport matrix is very sensitive to the type of dominant instability of the background turbulence. We present here a detailed quasi-linear gyrokinetic analysis of stationary turbulent particle transport by means of analytical and numerical calculations to show how the actual parametric dependence of the stationary normalized density gradient can strongly vary between an ion temperature gradient (ITG) dominated turbulence and a trapped electron mode dominated turbulence regime. It is also shown how the maximal achievable normalized density gradient is reached when the turbulence regime is in a mixed state. This result is interpreted as the interplay of different physical mechanisms arising from (linear) wave-particle resonances. The results presented here are addressed to interpret some of the still unresolved issues in interpreting known experimental results.