Effective Density of Non-Degenerate Random Walks on Homogeneous Spaces

Constantin Kogler, Wooyeon Kim

Abstract:

We prove effective density of random walks on homogeneous spaces, assuming that the underlying
measure is supported on matrices generating a dense subgroup and having algebraic entries. The
main novelty is an argument passing from high dimension to effective equidistribution in the setting
of random walks on homogeneous spaces, exploiting the spectral gap of the associated convolution
operator