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1 results

  • Phase transition in one-dimensional random walk with partially reflecting boundaries

  • Ora E. Percus
  • Journal:
    Advances in Applied Probability / Volume 17 / Issue 3 / September 1985
    Published online by Cambridge University Press:
    01 July 2016, pp. 594-606
    Print publication:
    September 1985

  • We consider an asymmetric random walk, with one or two boundaries, on a one-dimensional lattice. At the boundaries, the walker is either absorbed (with probability 1–ρ) or reflects back to the system (with probability p).

    The probability distribution (Pn(m)) of being at position m after n steps is obtained, as well as the mean number of steps before absorption. In the one-boundary case, several qualitatively different asymptotic forms of Pn(m) result, depending on the relationship between transition probability and the reflection probability.