Questions on DP, CRP and PYP

By Section 4 of [1], it seems that both CRP and PYP produces power-law distributions, where for CRP, the power-law exponent g=1, whereas for PYP it is 1+\alpha.

From the definition of DP, a generalization of Dirichlet distribution, DP should produce multinomial distributions.

But why is the relation between DP and CRP?

References:

  1. Producing power-law distributions and damping word frequencies with two-stage language models.