  We carry out multifractal analyses of multiple tracers namely the main galaxy
sample, the LRG sample and the quasar sample from the SDSS to test the
assumption of cosmic homogeneity and identify the scale of transition to
homogeneity, if any. We consider the behaviour of the scaled number counts and
the scaling relations of different moments of the galaxy number counts in
spheres of varying radius $R$ to calculate the spectrum of the
Minkowski-Bouligand general dimension $D_{q} (R)$ for $-4 \leq q \leq 4$. The
present analysis provides us the opportunity to study the spectrum of the
generalized dimension $D_{q}(R)$ for multiple tracers of the cosmic density
field over a wide range of length scales and allows us to confidently test the
validity of the assumption of cosmic homogeneity. Our analysis indicates that
the SDSS main galaxy sample is homogeneous on a length scales of $80\, h^{-1}\,
{\rm Mpc} $ and beyond whereas the SDSS quasar sample and the SDSS LRG sample
show transition to homogeneity on an even larger length scales at $\sim 150\,
h^{-1}\, {\rm Mpc}$ and $\sim 230\, h^{-1}\, {\rm Mpc}$ respectively. These
differences in the scale of homogeneity arise due to the effective mass and
redshift scales probed by the different tracers in a Universe where structures
form hierarchically. Our results reaffirm the validity of cosmic homogeneity on
large scales irrespective of the tracers used and strengthens the foundations
of the Standard Model of Cosmology.
