  Often the current mode coupling theory (MCT) of glass transitions is compared
with mean field theories. We explore this possible correspondence. After
showing a simple-minded derivation of MCT with some difficulties we give a
concise account of our toy model developed to gain more insight into MCT. We
then reduce this toy model by adiabatically eliminating rapidly varying
velocity-like variables to obtain a Fokker-Planck equation for the slowly
varying density-like variables where diffusion matrix can be singular. This
gives a room for nonergodic stationary solutions of the above equation.
