论文标题
Ramanujan图的熵证明
An entropic proof of cutoff on Ramanujan graphs
论文作者
论文摘要
Lubetzky和Peres最近证明了Ramanujan图上的简单随机步行表现出截止现象，也就是说，从均匀分布的随机步行分布的总变化距离从均匀分布突然从$ 1 $ $ 1 $下降到接近$ 0 $。这一事实已经有一些其他证据。在本说明中，我们基于功能分析和熵考虑提供了另一个证明。
It is recently proved by Lubetzky and Peres that the simple random walk on a Ramanujan graph exhibits a cutoff phenomenon, that is to say, the total variation distance of the random walk distribution from the uniform distribution drops abruptly from near $1$ to near $0$. There are already a few alternative proofs of this fact. In this note, we give yet another proof based on functional analysis and entropic consideration.
