A Law of Large Numbers for Local Patterns in Schur Measures and a Schur Process.

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability Pub Date : 2025-01-01 Epub Date: 2025-06-02 DOI:10.1007/s10959-025-01421-0
Pierre Lazag
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引用次数: 0

Abstract

The aim of this note is to prove a law of large numbers for local patterns in discrete point processes. We investigate two different situations: a class of point processes on the one-dimensional lattice including certain Schur measures, and a model of random plane partitions, introduced by Okounkov and Reshetikhin. The results state in both cases that the linear statistic of a function, weighted by the appearance of a fixed pattern in the random configuration and conveniently normalized, converges to the deterministic integral of that function weighted by the expectation with respect to the limit process of the appearance of the pattern.

舒尔测度中局部模式的大数定律和舒尔过程。
本文的目的是证明离散点过程中局部模式的一个大数定律。我们研究了两种不同的情况:一维晶格上的一类包含某些Schur测度的点过程,以及由Okounkov和Reshetikhin引入的随机平面划分模型。在这两种情况下,结果表明,一个函数的线性统计量,在随机构型中以固定模式的出现为权重并方便地归一化的情况下,收敛于该函数对模式出现的极限过程的期望加权的确定性积分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Theoretical Probability
Journal of Theoretical Probability 数学-统计学与概率论
CiteScore
1.50
自引率
12.50%
发文量
65
审稿时长
6-12 weeks
期刊介绍: Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.
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