The local limit theorem on nilpotent Lie groups
Probability
2021-05-25 v1
Abstract
A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization. The result extends an earlier local limit theorems of Alexopoulos which treated absolutely continuous measures with a continuous density of compact support, and also extends local limit theorems of Breuillard and Diaconis-Hough which treated general measures on the Heisenberg group.
Cite
@article{arxiv.1801.02530,
title = {The local limit theorem on nilpotent Lie groups},
author = {Robert Hough},
journal= {arXiv preprint arXiv:1801.02530},
year = {2021}
}