Compressed Random Variables in a Graph W*-Probability Space
  In this paper, we will consider the free probabilistic information about compressed random variables in a graph W*-Probability space. Recall the diagonal compressed random variables in a graph W*-probability space. In particular, we can see that the free moments and cumulants of the fixed compressed random variable of a random variable x are exactly same as the diagonal compressed part of x. 
Ilwoo Cho