Two One-dimensional Random Walk To The Square Root Of The Tail Probability Of Encounter Time Attenuation

This paper mainly research the hitting time of one-dimensional random walk .It is square root decline. We apply this into direction percolation. In Chapter 1, firstly, we clarify the paper's some preliminary results. Secondly,we introduce Markov Chain and random walk, large deviation and Skorohod Embedding. In Chapter 2,we used Skorohod Embedding and large deviation to derive criteria for the hitting time's square root decline.