随机有限多项式位势驻点的统计性质
Statistics of Stationary Points of Random Finite Polynomial Potentials
摘要：
多元随机势的势能面驻点在物理、化学和数学生物学等领域有着广泛的应用。然而，有几个可靠的方法，可以找到所有的SP准确。因此，人们必须依赖于间接的方法，如随机矩阵理论。结合数值多项式同伦延拓方法和认证方法，我们获得了所有认证的SP的最一般的多项式RP为每个样本选择的高斯分布的均值为0和方差为1。在有限尺寸RP情形下得到许多新结果的同时，我们还讨论了我们的结果对随机系统数学和弦论景观的影响。
英文摘要：
The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology. However, there are few reliable methods available which can find all the SPs accurately. Hence, one has to rely on indirect methods such as Random Matrix theory. With a combination of the numerical polynomial homotopy continuation method and a certification method, we obtain all the certified SPs of the most general polynomial RP for each sample chosen from the Gaussian distribution with mean 0 and variance 1. While obtaining many novel results for the finite size case of the RP, we also discuss the implications of our results on mathematics of random systems and string theory landscapes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
