论文标题
时刻和分支随机步行
Moments of Moments and Branching Random Walks
论文作者
论文摘要
我们计算出一个随机步行$ x_n（l）$的分支$ l $在二进制树上的深度$ n $上$β\ in \ Mathbb {r} $。我们为有限$ n $的最初几时刻获得了明确的公式。在极限$ n \ to \ infty $中，我们的表达与最近的猜想相吻合，结果是关于随机统一矩阵的特征多项式时刻的时刻，这支持了这两个问题，即这两个问题都属于对数上的高斯随机磁场的类别。
We calculate, for a branching random walk $X_n(l)$ to a leaf $l$ at depth $n$ on a binary tree, the positive integer moments of the random variable $\frac{1}{2^{n}}\sum_{l=1}^{2^n}e^{2βX_n(l)}$, for $β\in\mathbb{R}$. We obtain explicit formulae for the first few moments for finite $n$. In the limit $n\to\infty$, our expression coincides with recent conjectures and results concerning the moments of moments of characteristic polynomials of random unitary matrices, supporting the idea that these two problems, which both fall into the class of logarithmically correlated Gaussian random fields, are related to each other.
