A note on concentration functions on transformation groups
  In this note, we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$. We prove a necessary and sufficient condition for the concentration functions of a spread-out irreducible probability measure $\mu$ on $G$ to converge to zero. 
Mehrdad Kalantar and Mohammad S. M. Moakhar
math.DS