Poisson and Compound Poisson Approximations in a Nonconventional Setup
  We show that for all $\psi$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe completely the asymptotic behavior of these distributions. 
Yuri Kifer and Ariel Rapaport
math.PR math.DS