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arXiv · 2503.13361

Limit Theorems Under Several Linear Constraints

Fabrice Gamboa·Martin Venker
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Abstract

We study $n$ real-valued random variables subject to several linear constraints. Our main result is a weighted Central Limit Theorem, determining which linear combinations of these random variables are asymptotically normal as $n\to\infty$. Marginal distributions are also studied, showing that in the large $n$ limit random variables under linear constraints become i.i.d. exponential under a rescaling. Our novel approach is based on a complex de Finetti theorem revealing an underlying independence structure, as well as on entropy arguments.

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Fabrice Gamboa, Martin Venker. 2025-03-17. Limit Theorems Under Several Linear Constraints. https://arxiv.org/abs/2503.13361

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