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.
From: Martin Venker [view email]
[v1]
Mon, 17 Mar 2025 16:47:17 UTC (186 KB)
[v2]
Mon, 20 Jul 2026 14:09:06 UTC (190 KB)
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