A Limit Theorem for Shifted Schur Measures
A Limit Theorem for Shifted Schur Measures
复制标题
移位 Schur 测度的极限定理
DOI：
10.1215/s0012-7094-04-12316-4
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发表时间：
2002
影响因子：
2.5
通讯作者：
H. Widom
中科院分区：
文献类型：
--
作者：
C. Tracy;H. Widom
到每个分区λ=(λ1、λ2、.。。)对于不同的部分，我们指定概率Qλ(X)Pλ(Y)/Z，其中Qλ和Pλ是舒尔Q-函数，Z是归一化常数。这种度量，我们称之为移位Schur度量，类似于被广泛研究的Schur度量。对于x的前m个坐标和y的前n个坐标等于α(0<；α<；1)且其余坐标等于零的特化，我们导出了λ1的极限定律为m，n→∞，且τ=m/n固定。对于Schur测度，Johansson导出了α-特殊化极限律。我们的主要结果表明，这两个极限定律是相同的。
To each partition λ = (λ1, λ2, . . .) with distinct parts we assign the probability Qλ(x)Pλ(y)/Z where Qλ and Pλ are the Schur Q-functions and Z is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first m coordinates of x and the first n coordinates of y equal to α (0 < α < 1) and the rest equal to zero, we derive a limit law for λ1 as m, n → ∞ with τ = m/n fixed. For the Schur measure the α-specialization limit law was derived by Johansson. Our main result implies that the two limit laws are identical.