置换矩阵及其特征多项式的矩
概率论
2010-07-14 v2 数论
摘要
本文关注均匀测度下 n × n n\times n n × n Z n ( x ) Z_n(x) Z n ( x ) s k ∈ \Nr s_k\in\Nr s k ∈ \Nr \E ∏ k = 1 p Z n s k ( x k ) \E{\prod_{k=1}^p Z_n^{s_k}(x_k)} \E ∏ k = 1 p Z n s k ( x k ) max k ∣ x k ∣ < 1 \max_k|x_k|<1 max k ∣ x k ∣ < 1 lim n \rw ∞ \E ∏ k = 1 p Z n s k ( x k ) \lim_{n\rw\infty} \E{\prod_{k=1}^p Z_n^{s_k}(x_k)} lim n \rw ∞ \E ∏ k = 1 p Z n s k ( x k ) p = 2 , ∣ x 1 ∣ = ∣ x 2 ∣ = 1 p=2, |x_1|=|x_2|=1 p = 2 , ∣ x 1 ∣ = ∣ x 2 ∣ = 1 x 1 = x 2 ‾ x_1=\overline{x_2} x 1 = x 2 n \rw ∞ n\rw\infty n \rw ∞ s k ∈ \C s_k\in\C s k ∈ \C ∣ x ∣ < 1 |x|<1 ∣ x ∣ < 1 s ∈ \C s\in\C s ∈ \C Z ∞ s ( x ) Z_\infty^s(x) Z ∞ s ( x ) Z n s ( x ) → d Z ∞ s ( x ) Z_n^s(x)\xrightarrow{d}Z_\infty^s(x) Z n s ( x ) d Z ∞ s ( x ) max k ∣ x k ∣ < 1 \max_k|x_k|<1 max k ∣ x k ∣ < 1 n \rw ∞ n\rw\infty n \rw ∞ \E ∏ k = 1 p Z n s k ( x k ) \rw \E ∏ k = 1 p Z ∞ s k ( x k ) \E{\prod_{k=1}^p Z_n^{s_k}(x_k)}\rw \E{\prod_{k=1}^p Z_\infty^{s_k}(x_k)} \E ∏ k = 1 p Z n s k ( x k ) \rw \E ∏ k = 1 p Z ∞ s k ( x k )
引用
@article{arxiv.0910.5069,
title = {Permutation Matrices and the Moments of their Characteristic Polynomials},
author = {Dirk Zeindler},
journal= {arXiv preprint arXiv:0910.5069},
year = {2010}
}
备注
24 pages, 1 Figure