论文标题
Markov-Krein对应的量化类似物
A Quantized Analogue of the Markov-Krein Correspondence
论文作者
论文摘要
我们研究了一系列措施，该措施源于单位群体代表的不可约组成部分的签名，因为该组的规模属于无穷大。给定一个随机签名$λ$长度$ n $带有计数度量$ \ mathbf {m} $，我们通过投射到一个较低维度的单一组中获得了一个随机的签名$ n-1 $ $ n-1 $。签名$μ$与签名$λ$交织在一起，我们将$μ，λ$的数据记录在一个随机的矩形Young Dibargram $ W $中。我们表明，在$λ$的一定条件下，$ \ mathbf {m} $和$ w $ commente均为$ n \ to \ infty $。我们提供了限制对象之间生成函数关系的明确时刻。我们进一步表明，生成函数关系的力矩在有界度量和某些连续的年轻图之间引起了两次培养，可以将其视为马尔可夫·克雷因对应关系的量化类似物。
We study a family of measures originating from the signatures of the irreducible components of representations of the unitary group, as the size of the group goes to infinity. Given a random signature $λ$ of length $N$ with counting measure $\mathbf{m}$, we obtain a random signature $μ$ of length $N-1$ through projection onto a unitary group of lower dimension. The signature $μ$ interlaces with the signature $λ$, and we record the data of $μ,λ$ in a random rectangular Young diagram $w$. We show that under a certain set of conditions on $λ$, both $\mathbf{m}$ and $w$ converge as $N\to\infty$. We provide an explicit moment generating function relationship between the limiting objects. We further show that the moment generating function relationship induces a bijection between bounded measures and certain continual Young diagrams, which can be viewed as a quantized analogue of the Markov-Krein correspondence.
