No abstract uploaded!

The paper presents a study of Fuglede’s $p$ -module of systems of measures in condensers in polarizable Carnot groups. In particular, we calculate the $p$ -module of measures in spherical ring domains, find the extremal measures, and finally, extend a theorem by Rodin to these groups.

No abstract uploaded!

Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of results provide tight bounds on the average errors between empirical and population statistics of eigenvectors, fewer results are tight for entrywise analyses, which are critical for a number of problems such as community detection and ranking.

We give a complete classification of irreducible symmetric spaces for which there exist proper SL(2,R)-actions as isometries, using the criterion for proper actions by T. Kobayashi [Math. Ann. ’89] and combinatorial techniques of nilpotent orbits. In particular, we classify irreducible symmetric spaces that admit surface groups as discontinuous groups, combining this with Benoist’s theorem [Ann. Math. ’96].