蕾丝展开的一种广义归纳法
A generalised inductive approach to the lace expansion
摘要：
花边扩展是一个强大的工具，用于分析自我避免行走和渗流的临界行为。它产生了一个递归关系，我们抽象和研究使用适应的归纳法介绍了登霍兰德和作者。我们给出的条件下，该解决方案的递归关系的行为作为一个高斯，无论是在傅立叶空间和一个局部的中心极限定理。这些条件在其他地方示出，以保持足够的扩展模型的网络的自避免行走的尺寸$d>4$，并为临界导向渗流尺寸$d+1>5$，提供了一个统一的方法和一个重要的成分，详细分析这些模型的分支行为。
英文摘要：
The lace expansion is a powerful tool for analysing the critical behaviour of self-avoiding walks and percolation. It gives rise to a recursion relation which we abstract and study using an adaptation of the inductive method introduced by den Hollander and the authors. We give conditions under which the solution to the recursion relation behaves as a Gaussian, both in Fourier space and in terms of a local central limit theorem. These conditions are shown elsewhere to hold for sufficiently spread-out models of networks of self-avoiding walks in dimensions $d>4$, and for critical oriented percolation in dimensions $d+1>5$, providing a unified approach and an essential ingredient for a detailed analysis of the branching behaviour of these models.
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