  We discuss the emergence and growth of the cooperativity accompanying
vitrification based on the density fluctuation dynamics for fragile
glass-forming liquids. (i) The relaxation of density fluctuations proceeds by
the particle (density) exchange process, and is diffusive; that is, the
allowable kinetic paths are strongly restricted by the local conservation law.
(ii) In normal liquid states, this exchange process is less cooperative, and
the diffusion coefficient of density fluctuations $D_c$ is given as $D_c\sim
\lambda^2/\tau_\alpha$, where $\lambda$ is the particle size and $\tau_\alpha$
is the structural relaxation time. On the other hand, in supercooled states the
restriction on the kinetic path is more severe with increasing the degree of
supercooling, which makes the exchange process more cooperative, resulting in
$D_c \sim \xi_{\rm d}^2/\tau_\alpha$ with $\xi_{\rm d}$ being the cooperative
length scale. (iii) The molecular dynamics simulation results show that the
self-diffusion coefficient of the tagged particle, $D_s$, almost coincides with
$D_c$, suggesting that the collective density diffusion and the particle
diffusion closely share the same mechanism: in normal states $D_s$ determines
$D_c$, but vice versa in supercooled states. This immediately leads to the idea
that the breakdown of the Stokes-Einstein relation is not the anomaly in the
single-particle dynamics but reflects the increase in the cooperativity in the
density diffusion at the length scale of $\xi_{\rm d}$.
