On traversable length inside semi-cylinder in 2d supercritical bond percolation

Abstract

We investigate a limit theorem on traversable length inside semicylinder in the 2-dimensional supercritical Bernoulli bond percolation, which gives an extension of Theorem 2 in [5]. This type of limit theorems was originally studied for the extinction time for the 1-dimensional contact process on a finite interval in [10]. Actually, our main result Theorem 2.1 is stated under a rather general 2-dimensional bond percolation setting.