Applications of optimal transport to Dyson Brownian Motions and beyond
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866913846417948672 |
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| author | Wu, Xuan |
| author_facet | Wu, Xuan |
| contents | We develop a new method based on Caffarelli's contraction theorem in optimal transport to obtain sharp and uniform modulus of continuity estimates for $β$-Dyson Brownian motions with $β\geq 2$. Our method extends to a large class of random curve collections, which can be viewed as log-concave perturbations of Brownian motions, including the $β$-Dyson Brownian motion, the Air$\text{y}_β$ line ensemble, the KPZ line ensemble, and the O'Connell-Yor line ensemble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications of optimal transport to Dyson Brownian Motions and beyond Wu, Xuan Probability We develop a new method based on Caffarelli's contraction theorem in optimal transport to obtain sharp and uniform modulus of continuity estimates for $β$-Dyson Brownian motions with $β\geq 2$. Our method extends to a large class of random curve collections, which can be viewed as log-concave perturbations of Brownian motions, including the $β$-Dyson Brownian motion, the Air$\text{y}_β$ line ensemble, the KPZ line ensemble, and the O'Connell-Yor line ensemble. |
| title | Applications of optimal transport to Dyson Brownian Motions and beyond |
| topic | Probability |
| url | https://arxiv.org/abs/2412.17389 |