论文标题
高斯随机场与各向同性增量的复杂性
Complexity of Gaussian random fields with isotropic increments
论文作者
论文摘要
我们研究单个粒子模型在随机电位上的能量景观，也就是说，我们研究了$ x_n（x） +\ frac \ frac \ mu2 \ mu2 \ | x \ | x \ | x \ |^2，$ x__________________ {n} $的$ x_n（x） +\ frac \ mU2 \ |我们为开放式集合中的临界值的平均临界点的平均数量得出渐近公式，因为尺寸$ n $转到无限。在同伴论文中，我们为具有给定索引的临界点数量提供了相同的分析。
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a Gaussian process with isotropic increments. We derive asymptotic formulas for the mean number of critical points with critical values in an open set as the dimension $N$ goes to infinity. In a companion paper, we provide the same analysis for the number of critical points with a given index.
