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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2407.06593 |
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Table des matières:
- On the free, step $2$ Carnot groups of rank $n$ $\mathbb{G}_n$, the subRiemannian Brownian motion consists in a $\mathbb{R}^n$-Brownian motion together with its $\frac{n(n-1)}{2}$ L{é}vy areas. In this article we construct an explicit successful non co-adapted coupling of Brownian motions on $\mathbb{G}_n$. We use this construction to obtain gradient inequalities for the heat semi-group on all the homogeneous step $2$ Carnot groups. Comparing the first coupling time and the first exit time from a domain, we also obtain gradient inequalities for harmonic functions on $\mathbb{G}_n$. These results generalize the coupling strategy by Banerjee, Gordina and Mariano on the Heisenberg group.