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In this paper, we establish the super Poincar\'e inequality for thetwo-parameter Dirichlet process when the partition number of the state space isfinite. Furthermore, if the partition number is infinite, the super Poincar'einequality doesn't hold. To overcome the difficulty caused by the degenerencyof the diffusion coefficient on the boundary of the domain, localization methodand perturbation argument in [14] are effective.

Super Poincar'e inequality for a dynamic model for the two-parameter Dirichlet process