关于扩张图序列的局部弱极限的一个注记
A note on the local weak limit of a sequence of expander graphs
摘要：
证明了一列度一致有界的有限扩张图的局部弱极限是遍历（或极值）的单模随机图。特别地，极限随机图的临界渗流概率几乎必然是常数。作为推论，我们得到了Benjamini-Nacheland-Peres（2011）关于具有一致有界度的有限扩展图的渗流概率局部性的定理的改进，其中我们可以放弃极限是单个有根图的假设。
英文摘要：
We show that the local weak limit of a sequence of finite expander graphs with uniformly bounded degree is an ergodic (or extremal) unimodular random graph. In particular, the critical probability of percolation of the limiting random graph is constant almost surely. As a corollary, we obtain an improvement to a theorem by Benjamini-Nachmias-Peres (2011) on locality of percolation probability for finite expander graphs with uniformly bounded degree where we can drop the assumption that the limit is a single rooted graph.
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。
