Abstract

We consider a nearest neighbour random walk on the integers with absorption at 0 and constant jump probabilities to the left and right of zero. The associated spectral radius is ρ and → −∞ −∞ ∞ functions h−∞ and h+∞ associated with sequences xn converging to and + respectively. We construct a space-time sequence (xn, n) with xn converging to a point in the space-time the spatial ρ-Martin exit boundary comprises two extremal points and associated minimal excessive ρ-Martin exit boundary whose associated space time harmonic function h (x, t) is minimal and of the form ρ−th+∞(x) not ρ−th−∞ (x) as might have been hoped. J. San Martin acknowledges support from BASAL AFB170001.