  Mixtures of high dimensional Gaussian distributions have been studied
extensively in statistics and learning theory. While the total variation
distance appears naturally in the sample complexity of distribution learning,
it is analytically difficult to obtain tight lower bounds for mixtures.
Exploiting a connection between total variation distance and the characteristic
function of the mixture, we provide fairly tight functional approximations.
This enables us to derive new lower bounds on the total variation distance
between pairs of two-component Gaussian mixtures that have a shared covariance
matrix.
