论文标题
概率的翻新和分析延续
Probabilistic renormalization and analytic continuation
论文作者
论文摘要
我们介绍了串联概率重新归一化的理论，即在一组自然数对某个随机变量的期望中编码的重新归一化值。我们确定了一大批弱重新划分的Dirichlet类型，它们的分析取决于我们称为Bernoulli操作员的（无限级）差异操作员的属性。对于此类系列的系列，我们表明概率的重态化与分析延续兼容。 $ s \ neq 1 $的一般Zeta系列被认为是可重新分配的，其重新归一化的值由Riemann Zeta函数给出。
We introduce a theory of probabilistic renormalization for series, the renormalized values being encoded in the expectation of a certain random variable on the set of natural numbers. We identify a large class of weakly renormalizable series of Dirichlet type, whose analysis depends on the properties of a (infinite order) difference operator that we call Bernoulli operator. For the series in this class, we show that the probabilistic renormalization is compatible with analytic continuation. The general zeta series for $s\neq 1$ is found to be strongly renormalizable and its renormalized value is given by the Riemann zeta function.
