The limit theorems for the single point range of strongly transient random walks (Q1917000)

We study fluctuation problems of the single point range of strongly transient random walks. The single point range means the number of distinct sites entered once and only once by a random walk in the first \(n\) steps. The suitably normalized single point range is proved to converge to the standard normal random variable in the distribution sense, and moreover, we establish the law of the iterated logarithm.