  Brandenberger and Vafa have proposed the string cosmological model based on
T-duality. In this model, they took the toroidal target space and introduced
the new position \tilde{x} conjugate to the winding mode, in addition to the
position x conjugate to the momentum mode. In this way they can describe a
universe larger than the string scale with the coordinate x and one smaller
with the coordinate \tilde{x}. Resultingly, they never encounter the
singularity seen in the standard Big Bang scenario. The most interesting
phenomenon in this model is the transition from \tilde{x}-space to x-space when
the size of universe is nearly the string scale. Here, we define the dispersion
of the momentum number m times the winding number w as the `correlation' of
momentum modes and winding modes. Then using the statistical mechanics of
strings on a torus, we calculate the correlation in low and high temperature
limits, and we consider the possibility that we can observe this effect today,
but we will see that this is unlikely.
