冻结转移、随机矩阵的特征多项式和Riemann Zeta函数
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
摘要：
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，也决定了大N × N随机酉（CUE）矩阵的特征多项式的模的最大值的值分布。我们假定我们的结果推广到黎曼zeta函数zeta（s）在临界线s=1/2+it的定长截面上取的极值，并给出数值计算结果作为支持。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。
英文摘要：
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 (CUE) 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.
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