Erratum to “How many zeros of a random polynomial are real?”
Erratum to “How many zeros of a random polynomial are real?”
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DOI：
10.1090/s0273-0979-96-00678-7
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发表时间：
1995-01
影响因子：
1.3
通讯作者：
A. Edelman;E. Kostlan
中科院分区：
文献类型：
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作者：
A. Edelman;E. Kostlan
在文章“一个随机多项式有多少个零是真实的？”作者：Alan Edelman和Eric Kostlan（Bull. Amer. Math. Soc.（N.S.）32（1）（1995），1-37），我们的意思是说特征向量矩阵，而不是关联矩阵，是（1 1 1 - 1）n次的张量（或克罗内克）积。这个张量积是最简单的阿达玛矩阵。关联矩阵的特征值可以被看作是2k-n，其中k = 0，. . .，n.我们对第2.5节中的声明表示遗憾，即Kac公式渐近展开式中的常数C1不为先前的研究者所知。事实上，常数C1和进一步的渐近项是已知的威尔金斯[1]，谁也报告了以前的工作推导C1的Jamrom和王分别追溯到1971年和1983年。然而，我们相信我们的推导是新的。
In Section 4.3 of the article “How many zeros of a random polynomial are real?” by Alan Edelman and Eric Kostlan (Bull. Amer. Math. Soc. (N.S.) 32 (1) (1995), 1–37), we meant to say that the eigenvector matrix, not the incidence matrix, is the tensor (or Kronecker) product of ( 1 1 1 −1 ) n times. This tensor product is the simplest Hadamard matrix. The eigenvalues of the incidence matrix may then be seen to be 2k − n for k = 0, . . . , n. We regret the statement in Section 2.5 that the constant C1 in the asymptotic expansion of the Kac formula was unknown to previous researchers. Indeed the constant C1 and further asymptotic terms were known to Wilkins [1], who also reports on previous work deriving C1 by Jamrom and Wang going back to 1971 and 1983 respectively. We do believe, however, that our derivation is new.