The local limit theorem on nilpotent Lie groups

Robert Hough

doi:10.1007/s00440-018-0864-7

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arXiv · 1801.02530

The local limit theorem on nilpotent Lie groups

Robert Hough

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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.

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Robert Hough. 2018-01-08. The local limit theorem on nilpotent Lie groups. https://doi.org/10.1007/s00440-018-0864-7

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