论文标题
关于整数随机步行的速度的评论
Remarks on the speeds of a class of random walks on the integers
论文作者
论文摘要
近年来，人们有兴趣得出确定性概率的某些重要概率结果。例如，请参见\ cite {beig}和\ cite {acc}。在这项工作中，我们通过在整数上随机步行的速度与其范围的大小增长之间推断出众所周知的等效性，继续沿着这条道路。这个结果是凯斯滕·史激发 - 惠特曼定理的直接结果，并且通过出现本质上是概率的，但我们将表明它可以从基本的确定性结果中很容易遵循。我们还研究了零速度的复发随机步行的共同属性，并以示例表明该属性不必通过确定性序列共享。但是，如果我们考虑到达时间间的时间（序列等于0的时间），那么我们找到了一个足够的确定性条件，使得序列的速度为零，并证明这可以用于得出几个概率结果。
In recent years, there has been an interest in deriving certain important probabilistic results as consequences of deterministic ones; see for instance \cite{beig} and \cite{acc}. In this work, we continue on this path by deducing a well known equivalence between the speed of random walks on the integers and the growth of the size of their ranges. This result is an immediate consequence of the Kesten-Spitzer-Whitman theorem, and by appearances is probabilistic in nature, but we will show that it follows easily from an elementary deterministic result. We also investigate the common property of recurrent random walks of having speed zero, and show by example that this property need not be shared by deterministic sequences. However, if we consider the inter-arrival times (times at which the sequence is equal to 0) then we find a sufficient deterministic condition for a sequence to have zero speed, and show that this can be used to derive several probabilistic results.
