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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2403.10724 |
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| _version_ | 1866913267115360256 |
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| author | Budway, Benjamin Shkolnikov, Mykhaylo |
| author_facet | Budway, Benjamin Shkolnikov, Mykhaylo |
| contents | Multilevel Dyson Brownian motions (MDBMs) combine Dyson Brownian motions of different dimensions into a single process in a canonical way. This paper completes the theory of MDBMs for $β\ge2$. Specifically, we use the superposition principle of Figalli and Trevisan to construct the MDBMs for all $β>2$ in a unified manner. This also extends their stochastic differential equation representation, first discovered by Gorin and Shkolnikov, to all $β>2$ and proves the uniqueness of the MDBMs for all $β>2$. Finally, we show that their limit as $β\downarrow2$ is given by the $β=2$ MDBM, commonly referred to as the Warren process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multilevel Dyson Brownian motions via the superposition principle Budway, Benjamin Shkolnikov, Mykhaylo Probability 60H Multilevel Dyson Brownian motions (MDBMs) combine Dyson Brownian motions of different dimensions into a single process in a canonical way. This paper completes the theory of MDBMs for $β\ge2$. Specifically, we use the superposition principle of Figalli and Trevisan to construct the MDBMs for all $β>2$ in a unified manner. This also extends their stochastic differential equation representation, first discovered by Gorin and Shkolnikov, to all $β>2$ and proves the uniqueness of the MDBMs for all $β>2$. Finally, we show that their limit as $β\downarrow2$ is given by the $β=2$ MDBM, commonly referred to as the Warren process. |
| title | Multilevel Dyson Brownian motions via the superposition principle |
| topic | Probability 60H |
| url | https://arxiv.org/abs/2403.10724 |