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A hierarchical model for random walks in random media

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Abstract

We show that the random walk generated by a hierarchical Laplacian in ℤd has standard diffusive behavior. Moreover, we show that this behavior is stable under a class of random perturbations that resemble an off-diagonal disordered lattice Laplacian. The density of states and its asymptotic behavior around zero energy are computed: singularities appear in one and two dimensions.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas de São Carlos, Universidade de São Paulo, 13560, São Carlos, SP, Brazil

    Cláudio Paiva

  2. Instituto de Física, Universidade de São Paulo, 01498-970, São Paulo, SP, Brazil

    J. Fernando Perez

Authors
  1. Cláudio Paiva
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  2. J. Fernando Perez
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Paiva, C., Perez, J.F. A hierarchical model for random walks in random media. J Stat Phys 71, 435–452 (1993). https://doi.org/10.1007/BF01058431

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  • DOI: https://doi.org/10.1007/BF01058431

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