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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2503.13132 |
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| _version_ | 1866918065174740992 |
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| author | Jin, Bochen |
| author_facet | Jin, Bochen |
| contents | We investigate the limiting behaviour of the path of random bridges treated as random sets in $\mathbb{R}^{d}$ with the Euclidean metric and the dimension $d$ increasing to infinity. The main result states that, in the square integrable case, the limit (in the Gromov-Hausdorff sense) is deterministic, namely, it is $[0,1]$ equipped with the pseudo-metric $\sqrt{|t-s|(1-|t-s|)}$. We also show that, in the heavy-tailed case with summands regularly varying of order $α\in (0,1)$, the limiting metric space has a random metric derived from the bridge variant of a subordinator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random Bridges in Spaces of Growing Dimension Jin, Bochen Probability 60F05 60G50 We investigate the limiting behaviour of the path of random bridges treated as random sets in $\mathbb{R}^{d}$ with the Euclidean metric and the dimension $d$ increasing to infinity. The main result states that, in the square integrable case, the limit (in the Gromov-Hausdorff sense) is deterministic, namely, it is $[0,1]$ equipped with the pseudo-metric $\sqrt{|t-s|(1-|t-s|)}$. We also show that, in the heavy-tailed case with summands regularly varying of order $α\in (0,1)$, the limiting metric space has a random metric derived from the bridge variant of a subordinator. |
| title | Random Bridges in Spaces of Growing Dimension |
| topic | Probability 60F05 60G50 |
| url | https://arxiv.org/abs/2503.13132 |