Journal of Statistical Physics

, Volume 9, Issue 2, pp 101–135 | Cite as

Random walks on lattices. IV. Continuous-time walks and influence of absorbing boundaries

  • Elliott W. Montroll
  • Harvey Scher


The general study of random walks on a lattice is developed further with emphasis on continuous-time walks with an asymmetric bias. Continuous time walks are characterized by random pauses between jumps, with a common pausing time distributionψ(t). An analytic solution in the form of an inverse Laplace transform for P(l, t), the probability of a walker being atl at timet if it started atlo att=0, is obtained in the presence of completely absorbing boundaries. Numerical results for P(l, t) are presented for characteristically different ψ(t), including one which leads to a non-Gaussian behavior for P(l, t) even for larget. Asymptotic results are obtained for the number of surviving walkers and the mean 〈l〉 showing the effect of the absorption at the boundary.

Key words

Random walks transport theory stochastic processes boundary value problems continuous-time walks 


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Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • Elliott W. Montroll
    • 1
  • Harvey Scher
    • 2
  1. 1.Institute for Fundamental Studies, Department of Physics and AstronomyUniversity of RochesterRochester
  2. 2.Xerox Rochester Research CenterRochester

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