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

TL;DR

This paper proves the super Poincaré inequality for the two-parameter Dirichlet process with finite partitions, highlighting the boundary degeneracy challenge and employing localization and perturbation methods.

Contribution

It establishes conditions under which the super Poincaré inequality holds for the two-parameter Dirichlet process, especially for finite partitions.

Findings

Super Poincaré inequality holds for finite partitions.

Inequality does not hold for infinite partitions.

Localization and perturbation methods effectively address boundary degeneracy.

Abstract

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