Weighted Super Poincare Inequalities for Infinite-Dimensional Extension of the Dirichlet Distribution
Weiwei Zhang
TL;DR
This paper establishes weighted super Poincare inequalities for the infinite-dimensional Dirichlet distribution extension, addressing the failure of standard inequalities and providing new mathematical tools.
Contribution
It introduces weighted super Poincare inequalities tailored for the infinite-dimensional Dirichlet distribution extension, overcoming previous limitations.
Findings
Weighted super Poincare inequalities are established for the measure.
Two different Dirichlet forms are considered.
The inequalities address the non-validity of standard super Poincare inequalities.
Abstract
For the infinite-dimensional extension of the Dirichlet distribution, the super Poincare inequality does not hold based on the result in [14], so we establish the weighted super Poincare inequalities for this measure with respect to two different Dirichlet forms respectively.
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Taxonomy
TopicsMathematical Inequalities and Applications · Point processes and geometric inequalities · Mathematical Approximation and Integration