2021/05/09 by Esther Bou Dagher, Dagher, Esther Bou, Bogusław Zegarliński +1
Mathematics · #22E30 #26D10 #39B62 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2105.03922
openalex publication_date 2021/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.