划分上的马尔可夫过程
Markov processes on partitions
摘要：
本文引入并研究了一类划分上的马尔可夫过程。该过程保留了所谓的Z-措施分区先前研究的调和分析上的无限对称群。我们证明了这些过程的动态关联函数具有行列式结构，并明确地计算了它们的关联核。我们还计算了在两个不同的制度的内核的缩放限制。极限核描述了相应的随机Young图的大行和大列的渐近行为，以及Young图在对角线附近的行为。我们的研究结果表明，最近发现的类比表示理论中产生的随机分区和随机矩阵的频谱扩展到相关的时间依赖模型。
英文摘要：
We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group. We show that the dynamical correlation functions of these processes have determinantal structure and we explicitly compute their correlation kernels. We also compute the scaling limits of the kernels in two different regimes. The limit kernels describe the asymptotic behavior of large rows and columns of the corresponding random Young diagrams, and the behavior of the Young diagrams near the diagonal. Our results show that recently discovered analogy between random partitions arising in representation theory and spectra of random matrices extends to the associated time-dependent models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
