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  • 1
    Electronic Resource
    Electronic Resource
    Fractal and lacunary stochastic processes (1983)
    Springer
    Journal of statistical physics 30 (1983), S. 273-283 
    Details
    ISSN: 1572-9613
    Keywords: Random walks ; fractals ; stable distributions ; lacunary series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Discrete-time random walks simulate diffusion if the single-step probability density function (jump distribution) generating the walk is sufficiently shortranged. In contrast, walks with long-ranged jump distributions considered in this paper simulate Lévy or stable processes. A one-dimensional walk with a selfsimilar jump distribution (the Weierstrass random walk) and its higherdimensional generalizations generate fractal trajectories if certain transience criteria are met and lead to simple analogs of deep results on the Hausdorff-Besicovitch dimension of stable processes. The Weierstrass random walk is lacunary (has gaps in the set of allowed steps) and its characteristic function is Weierstrass' non-differentiable function. Other lacunary random walks with characteristic functions related to Riemann's zeta function and certain numbertheoretic functions have very interesting analytic structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012302
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Two-component ising chain with nearest-neighbor interaction (1973)
    Springer
    Journal of statistical physics 8 (1973), S. 309-333 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; disordered system ; one-dimensional chain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The one-dimensional, two-component linear Ising chain with nearest-neighbor interaction is formulated by using the transfer matrix method, with emphasis placed on the case in which the two components are randomly distributed along the chain. Certain recurrence formulas appear such that themth-order partition function of one of the components is dependent on the lower-order ones. The algorithm provides a working basis for discussing the thermodynamic and magnetic functions with various concentrations of one of the components. An exact expression for the partition function is derived for a linear chain which is composed of a periodic distribution of the two components. The construction of a periodic sequence which would approximate a random distribution of the two components is briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020270
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    Paper (German National Licenses)
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