Asymptotic Behaviors of The Size of The Largest Cluster in One Dimensional Percolation

Abstract

This paper focuses on the asymptotic behaviors of the length of the largest 1-cluster in a finite iid Bernoulli sequence. We first reveal a critical phenomenon on the length and then study its limit distribution.

This paper has been withdrawn by the auther. Because the main result (Theorem 1.1) is not new, it was first proved by Erdos and Renyi (1970) and is called the Erdos-Renyi Law