Dimension spectrum for a nonconventional ergodic average
  We compute the dimension spectrum of certain nonconventional averages, namely, the Hausdorff dimension of the set of $0,1$ sequences, for which the frequency of the pattern 11 in positions $k, 2k$ equals a given number $\theta\in [0,1]$. 
Yuval Peres, Boris Solomyak
math.DS