Large deviations principle for sub-Riemannian random walks

Maria Gordina; Tai Melcher; Dan Mikulincer; Jing Wang

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arXiv · 2210.05817

Large deviations principle for sub-Riemannian random walks

Maria Gordina·Tai Melcher·Dan Mikulincer·Jing Wang

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Abstract

We study large deviations for random walks on stratified (Carnot) Lie groups. For such groups, there is a natural collection of vectors which generates their Lie algebra, and we consider random walks with increments in only these directions. Under certain constraints on the distribution of the increments, we prove a large deviation principle for these random walks with a natural rate function adapted to the sub-Riemannian geometry of these spaces.

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Maria Gordina, Tai Melcher, Dan Mikulincer, Jing Wang. 2022-10-11. Large deviations principle for sub-Riemannian random walks. https://arxiv.org/abs/2210.05817

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