具有截断现象的显式展开式
Explicit expanders with cutoff phenomena
摘要：
截断现象描述了遍历有限马尔可夫链收敛到平衡点的急剧转变。特别感兴趣的是理解这种收敛的简单随机游动上的有界度扩展图。第一个例子的家庭的有界度图的随机游动展品切断全变差是最近才提供的，当作者表明这是一个典型的随机正则图。然而，没有一个例子是已知的显式（确定性）家庭的扩张与这种现象。在这里，我们构建了一个家庭的立方扩张的随机游动从最坏的情况下的初始位置表现出全变差截止。这种构造的变体给出了没有截止的三次扩张器，以及在任何指定时间点截止的三次图。
英文摘要：
The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph. The first example of a family of bounded-degree graphs where the random walk exhibits cutoff in total-variation was provided only very recently, when the authors showed this for a typical random regular graph. However, no example was known for an explicit (deterministic) family of expanders with this phenomenon. Here we construct a family of cubic expanders where the random walk from a worst case initial position exhibits total-variation cutoff. Variants of this construction give cubic expanders without cutoff, as well as cubic graphs with cutoff at any prescribed time-point.
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