We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimension-free and depend on the nuclear (Schatten-one) norm of the difference between the...

In the work a characterization of difference of multivariate Gaussian measures is found on the family of centered Eucledian balls. In particular, it helps to derive (xx see paper).

Housing typically takes up a major proportion of households' expenditure, and thus it certainly plays a critical role in shaping the pattern of income inequality and social mobility. Whether high housing price-to-rent ratio will am- plify inequality and inhibit social class upgrading is still a...