Fluctuations of particle systems determined by Schur generating functions
Fluctuations of particle systems determined by Schur generating functions
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DOI：
10.1016/j.aim.2018.07.009
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发表时间：
2016-04
影响因子：
1.7
通讯作者：
Alexey Bufetov;V. Gorin
中科院分区：
文献类型：
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作者：
Alexey Bufetov;V. Gorin
我们开发了一个新的工具箱，用于分析随机离散粒子系统的全局行为。本文引入并研究了随机离散组态的Schur母函数的概念。我们的主要结果提供了一个中心极限定理（CLT）这样的配置给定一定的条件下的舒尔生成函数。作为这种方法的应用，我们证明了CLT的几个概率模型来自渐近表示理论和统计物理，包括随机菱形和多米诺瓷砖，不相交的随机游动，分解的张量积的酉群的表示。
We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a Central Limit Theorem (CLT) for such a configuration given certain conditions on the Schur generating function. As applications of this approach, we prove CLT's for several probabilistic models coming from asymptotic representation theory and statistical physics, including random lozenge and domino tilings, non-intersecting random walks, decompositions of tensor products of representations of unitary groups.