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arXiv · 2605.15783

Set-indexed and multiple sums in high dimensions

Bochen Jin·Alexander Marynych·Ilya Molchanov
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Abstract

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.

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Bochen Jin, Alexander Marynych, Ilya Molchanov. 2026-05-15. Set-indexed and multiple sums in high dimensions. https://arxiv.org/abs/2605.15783

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