Abstract：

In the divergence case of Khintchine’s theorem, Schmidt obtained an asymptotic formula for the number of rational approximations of bounded height to almost every real number. We prove an analogue of this result for intrinsic Diophantine approximation on Grassmannians. The proof relies on analytic properties of a new Siegel transform naturally associated with the Grassmannian, together with exponential mixing in the space of lattices.