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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2305.18996 |
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| _version_ | 1866914635473485824 |
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| author | Clausel, Marianne Diehl, Joscha Mignot, Raphael Schmitz, Leonard Sugiura, Nozomi Usevich, Konstantin |
| author_facet | Clausel, Marianne Diehl, Joscha Mignot, Raphael Schmitz, Leonard Sugiura, Nozomi Usevich, Konstantin |
| contents | We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). We provide two algorithms for computing it, using methods from Lie theory (namely, the Baker-Campbell-Hausdorff formula) and from the theory of Gröbner bases of modules. Our main motivation stems from measures induced by iterated-integrals signatures, and we calculate the barycenter for the signature of the Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18996 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures Clausel, Marianne Diehl, Joscha Mignot, Raphael Schmitz, Leonard Sugiura, Nozomi Usevich, Konstantin Rings and Algebras 60L10 (Primary) 22E25, 60J65, 13P10, 15A69 (Secondary) We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). We provide two algorithms for computing it, using methods from Lie theory (namely, the Baker-Campbell-Hausdorff formula) and from the theory of Gröbner bases of modules. Our main motivation stems from measures induced by iterated-integrals signatures, and we calculate the barycenter for the signature of the Brownian motion. |
| title | The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures |
| topic | Rings and Algebras 60L10 (Primary) 22E25, 60J65, 13P10, 15A69 (Secondary) |
| url | https://arxiv.org/abs/2305.18996 |