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  • 1
    Electronic Resource
    Electronic Resource
    A simple calculation for the average number of steps to trapping in lattice random walks (1976)
    Springer
    Journal of statistical physics 15 (1976), S. 393-397 
    Details
    ISSN: 1572-9613
    Keywords: Random walk ; steps to trapping ; lattice walk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that the asymptotic results for the average number of steps to trapping at an irreversible trapping site on aD-dimensional finite lattice can be obtained from the generating function for random walks on aninfinite perfect lattice. This introduces a significant simplification into such calculations. An interesting corollary of these calculations is the conclusion that a random walker traverses, on the average, all the distinct nontrapping lattice sites before arriving on the trapping site.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020341
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Studies in nonlinear stochastic processes. IV. A comparison of statistical linearization, diagrammatic expansion, and projection operator methods (1978)
    Springer
    Journal of statistical physics 18 (1978), S. 217-233 
    Details
    ISSN: 1572-9613
    Keywords: Stochastic processes ; nonlinear processes ; statistical linearization ; perturbation expansions ; projection operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We compare the methods of statistical linearization, perturbation expansions, and projection operators for the approximate solution of nonlinear multimode stochastic equations. The model equations we choose for this comparison are coupled, nonlinear, first-order, one-dimensional complex mode rate equations. We show that the method of statistical linearization is completely equivalent to the neglect of certain well-defined diagrams in the perturbation expansion resulting in the first Kraichnan-Wyld approximation, and to the retention of only Markovian terms in the projection operator method, i.e., those terms that are local in time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014312
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Random walks on periodic and random lattices. II. Random walk properties via generating function techniques (1979)
    Springer
    Journal of statistical physics 21 (1979), S. 517-548 
    Details
    ISSN: 1572-9613
    Keywords: Random walks ; periodic lattices ; random lattices ; generating function techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the random walk properties of a class of two-dimensional lattices with two different types of columns and discuss the dependence of the properties on the densities and detailed arrangements of the columns. We show that the row and column components of the mean square displacement are asymptotically independent of the details of the arrangement of columns. We reach the same conclusion for some other random walk properties (return to the origin and number of distinct sites visited) for various periodic arrangements of a given relative density of the two types of columns. We also derive exact asymptotic results for the occupation probabilities of the two types of distinct sites on our lattices which validate the basic conjecture on bond and step ratios made in the preceding paper in this series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011166
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    Paper (German National Licenses)
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