Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta Function
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta Function
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DOI：
10.1103/physrevlett.108.170601
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发表时间：
2012-04-26
影响因子：
8.6
通讯作者：
Keating, Jonathan P.
中科院分区：
文献类型：
--
作者：
Fyodorov, Yan V.;Hiary, Ghaith A.;Keating, Jonathan P.
我们认为，冻结过渡的情况下，以前探索的统计力学的1/f噪声随机能量模型，也决定了最大值分布的大N × N随机酉矩阵的特征多项式的模。我们假设我们的结果扩展到黎曼zeta函数zeta（s）在临界线s 1/2 +它的恒定长度的部分所采取的极值，并提出了支持的数值计算结果。我们的主要目的是提请注意随机能量景观的统计力学，随机矩阵理论和黎曼zeta函数的理论之间可能的联系。
We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large N x N random unitary matrices. We postulate that our results extend to the extreme values taken by the Riemann zeta function zeta(s) over sections of the critical line s 1/2 + it of constant length and present the results of numerical computations in support. Our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes, random-matrix theory, and the theory of the Riemann zeta function.