论文标题
Riesz型气体的普遍运输不平等和浓度界限
Generalized transport inequalities and concentration bounds for Riesz-type gases
论文作者
论文摘要
本文探讨了广义的Riesz电能与规范对双重性定义的概率度量的联系。我们得出了连接这两个概念的功能不平等，从而恢复和推广现有的库仑运输不平等。然后，我们使用它们来证明围绕平衡和热平衡度量的度量浓度。最后，我们利用这些浓度的不平等能力获得Moser-Trudinger-type不等式，这也可以解释为波动的拉普拉斯变换的界限。
This paper explores the connection between a generalized Riesz electric energy and norms on the set of probability measures defined in terms of duality. We derive functional inequalities linking these two notions, recovering and generalizing existing Coulomb transport inequalities. We then use them to prove concentration of measure around the equilibrium and thermal equilibrium measures. Finally, we leverage these concentration inequalities to obtain Moser-Trudinger-type inequalities, which may also be interpreted as bounds on the Laplace transform of fluctuations.
