ISSN:
1572-9613
Keywords:
Random walks
;
stochastic processes
;
exponential models
;
mean first passage time
;
branching ratio
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01011697
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