特征多项式的矩枚举二行字典阵列
Moments of characteristic polynomials enumerate two-rowed lexicographic arrays
摘要:
给出了随机酉矩阵特征多项式矩的一种组合解释。这导致了Keating和Snaith猜想的一个相当意想不到的结果:$\midξ(1/2+it)\mid$的矩被证明与一些增加的连续性问题(如最后一次通过渗流问题)有关。
英文摘要:
A combinatorial interpretation is provided for the moments of characteristic polynomials of random unitary matrices. This leads to a rather unexpected consequence of the Keating and Snaith conjecture: the moments of $\midξ(1/2+it)\mid$ turn out to be connected with some increasing subsequences problems (such as the last passage percolation problem).
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