标题： 标准杨表的全局波动 显示英文标题

标题： Global fluctuations for standard Young tableaux

摘要： 我们引入了整数分拆上概率测度的Young生成函数的概念。 我们使用这个对象来表征满足大数定律和满足中心极限定理的概率分布。 我们进一步建立了多层级中心极限定理，这使得可以研究随机标准Young表。 作为这些结果的应用，我们描述了与以下情况相关的高度函数的波动：(i) Plancherel增长过程，(ii) 固定形状的随机标准Young表，以及(iii) 由无限对称群的极端特征诱导的概率分布$S_\infty$。 在所有情况下，我们将极限波动识别为条件高斯自由场。 显示英文摘要

摘要： We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that satisfy a central limit theorem. We further establish a multilevel central limit theorem, which enables the study of random standard Young tableaux. As applications of these results, we describe the fluctuations of height functions associated with (i) the Plancherel growth process, (ii) random standard Young tableaux of fixed shape, and (iii) probability distributions induced by extreme characters of the infinite symmetric group $S_\infty$. In all cases, we identify the limiting fluctuations as a conditioned Gaussian Free Field.