马洛尺度的局部中心极限定理

arXiv - MATH - Probability Pub Date : 2024-09-16 DOI:arxiv-2409.10415

Alexey Bufetov, Kailun Chen

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引用次数: 0

摘要

我们在 Starr（2009）的极限开创中研究了关于排列的 Mallows 度量的统计。我们的主要结果是其高度函数的局部中心极限定理。我们还重新推导了大数定律和大偏差原理的版本，从局部中心极限定理得到了标准中心极限定理，并建立了局部中心极限定理的多点版本。

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Local central limit theorem for Mallows measure

We study the statistics of the Mallows measure on permutations in the limit pioneered by Starr (2009). Our main result is the local central limit theorem for its height function. We also re-derive versions of the law of large numbers and the large deviation principle, obtain the standard central limit theorem from the local one, and establish a multi-point version of the local central limit theorem.

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arXiv - MATH - Probability

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