Limit Theorems Under Several Linear Constraints

2025/03/17 by Fabrice Gamboa, Martin Venker, Gamboa, Fabrice +1
Mathematics · #math.PR

paper · pdf · doi:10.48550/arxiv.2503.13361

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→∞. 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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