  By the collective name of {\it lattice counting} we refer to a setup
introduced in Duke-Rudnick-Sarnak that aim to establish a relationship between
arithmetic and randomness in the context of affine symmetric spaces. In this
paper we extend the geometric setup from symmetric to real spherical spaces and
continue to develop the approach with harmonic analysis which was initiated in
Duke-Rudnick-Sarnak.

Representation Theory