Stationary Probability and First-Passage Time of Biased Random Walk*

In this paper, we consider the stationary probability and first-passage time of biased random walk on ID chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0 <= p,q <= 1, p q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F similar to (N - 1)(gamma), where the exponent gamma = 2 for N < - vertical bar P - q vertical bar(-1) and gamma = 1 for N > - vertical bar P - q vertical bar(-1) Our study sheds useful insights into the biased random-walk process.