Rational-ray escape-of-mass conjecture

Let $\Omega$ be the space of rays, let $\xi\in\Omega$ be rational, and let $\mu_{x_n^\xi}$ be the associated sequence of measures on the homogeneous space $X_\infty$.

Rational-ray escape-of-mass conjecture. For any rational $\xi\in\Omega$, the measures $\mu_{x_n^\xi}$ converge to the zero measure.

This conjecture concerns the exceptional behaviour of rational rays and expresses complete escape of mass along them. The source introduces it after the generic equidistribution conjecture as a suggestion based on computer experiments; its resolution is not established in the supplied text.