Coercive inequalities on Carnot groups: taming singularities

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-12 DOI:10.1007/s13324-024-00908-z

E. Bou Dagher, B. Zegarliński

引用次数: 0

Abstract

In the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. To this end, we develop a technique to introduce natural singularities in the energy function U in order to force one of the coercivity conditions. In particular, we explore explicit constructions of probability measures on Carnot groups which secure Poincaré and even Logarithmic Sobolev inequalities. As applications, we get analogues of the Dyson–Ornstein–Uhlenbeck model on the Heisenberg group and obtain results on the discreteness of the spectrum of related Markov generators.

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卡诺群上的强制不等式：驯服奇点

在卡诺方程组的背景下，我们提出了一种驯服奇异性以获得矫顽力不等式的方法。为此，我们开发了一种在能量函数 U 中引入自然奇点的技术，以强制其中一个强制条件。特别是，我们探索了卡诺群上概率度量的明确构造，它确保了波恩卡列不等式，甚至对数索波列夫不等式。作为应用，我们得到了海森堡群上的戴森-奥恩斯坦-乌伦贝克模型的类比，并获得了相关马尔可夫发电机谱的离散性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.