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Eigenfunction approach to the persistent random walk in two dimensions

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  • Bracher, Christian

Abstract

The Fourier–Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,φ) encountered in a planar persistent random walk, where the direction taken in a step depends on the relative orientation towards the preceding step. For all but the shortest walks, the proposed method provides a rapidly converging, numerically stable algorithm that is particularly useful for the precise study of intermediate-size chains that have not yet approached the diffusion limit.a

Suggested Citation

  • Bracher, Christian, 2004. "Eigenfunction approach to the persistent random walk in two dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 448-466.
    • Handle: RePEc:eee:phsmap:v:331:y:2004:i:3:p:448-466
    DOI: 10.1016/j.physa.2003.07.003
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    References listed on IDEAS

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    1. Weiss, George H. & Shmueli, Uri, 1987. "Joint densities for random walks in the plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 641-649.
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    Cited by:

    1. Nogueira, Isadora R. & Alves, Sidiney G. & Ferreira, Silvio C., 2011. "Scaling laws in the diffusion limited aggregation of persistent random walkers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4087-4094.

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