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Biased random walk on a multidimensional lattice with absorbing boundaries

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  • Prasad, M.A.
  • Unnikrishnan, K.

Abstract

This paper deals with continuous-time random walk on a hypercubic lattice with absorbing boundaries along the axial planes through the origin. Possible bias in the transition probabilities along any axis is allowed for. Any dynamical model which is solvable in the case of an infinite lattice is shown to be tractable also in the present case. As an example, the exponential holding time model is solved explicitly. Representative numerical results for the probability of return to the starting point and the probability of absorption are presented for the one-dimensional case. It is found that, unlike the absorption which increases with bias towards the boundary, the return probability is independent of the direction of the bias.

Suggested Citation

  • Prasad, M.A. & Unnikrishnan, K., 1984. "Biased random walk on a multidimensional lattice with absorbing boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(3), pages 659-666.
    • Handle: RePEc:eee:phsmap:v:127:y:1984:i:3:p:659-666
    DOI: 10.1016/0378-4371(84)90049-9
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    1. James S. Plaxico & Daryll E. Ray, 1973. "Implications for Agricultural Economists," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 55(3), pages 399-403.
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