7 citations · 20 across the 5 of their papers we have counts for
5 papers
Expanding measures: Random walks and rigidity on homogeneous spaces
Roland Prohaska, Cagri Sert, Ronggang Shi
Let be a real Lie group, a lattice and a connected semisimple subgroup without compact factors and with finite center. We define the notion of -expanding measure…
On Convergence of Random Walks on Moduli Space
Roland Prohaska
The purpose of this note is to establish convergence of random walks on the moduli space of Abelian differentials on compact Riemann surfaces in two different modes: convergence of…
Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces
Roland Prohaska
We investigate three aspects of weak* convergence of the -step distributions of random walks on finite volume homogeneous spaces of semisimple real Lie groups. First, we l…
Spread Out Random Walks on Homogeneous Spaces
Roland Prohaska
A measure on a locally compact group is called spread out if one of its convolution powers is not singular with respect to Haar measure. Using Markov chain theory, we conduct a det…
Markov Random Walks on Homogeneous Spaces and Diophantine Approximation on Fractals
Roland Prohaska, Cagri Sert
In a first part, using the recent measure classification results of Eskin--Lindenstrauss, we give a criterion to ensure a.s. equidistribution of empirical measures of an i.i.d. ran…