Another look at independence of hitting place and time for the simple random walk

AbstractResults of Samuels and Wendel for the simple random walk with drift on the integers which assert independence of interarrival times at the sets {a−r, a+r}, r=1, 2…, k and the arrival position in the set {a−k,a+k}, where a is the starting point, are reobtained by treating the walk as a Markov chain, and considering related chains conditional on absorption at a specified barrier