Set-indexed and multiple sums in high dimensions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918503502577664 |
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| author | Jin, Bochen Marynych, Alexander Molchanov, Ilya |
| author_facet | Jin, Bochen Marynych, Alexander Molchanov, Ilya |
| contents | We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is identified as a generalisation of the Wiener spiral, which appears as the high-dimensional limit of single-index sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15783 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Set-indexed and multiple sums in high dimensions Jin, Bochen Marynych, Alexander Molchanov, Ilya Probability Primary 60G50, 60G60, Secondary 62G30 We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is identified as a generalisation of the Wiener spiral, which appears as the high-dimensional limit of single-index sums. |
| title | Set-indexed and multiple sums in high dimensions |
| topic | Probability Primary 60G50, 60G60, Secondary 62G30 |
| url | https://arxiv.org/abs/2605.15783 |