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Joint distribution function for position and rotation angle in plane random walks

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  • Wille, L.T.

Abstract

The angle by which the tangent to the trajectory rotates in the course of a plane random walk is studied. The joint probability distribution function for position and rotation angle in a random walk of n steps is obtained in closed form. This result is a generalization of Kluyver's integral representation for the distribution function of the position alone. Explicit expressions are presented for n = 1, 2 and n → ∞, in the latter case both by application of the central limit theorem and the steepest descent method. The distribution of the rotation angle modulo 2π is also discussed and turns out to be particularly simple.

Suggested Citation

  • Wille, L.T., 1987. "Joint distribution function for position and rotation angle in plane random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(2), pages 509-523.
    • Handle: RePEc:eee:phsmap:v:141:y:1987:i:2:p:509-523
    DOI: 10.1016/0378-4371(87)90178-6
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    1. Wille, L.T. & Vennik, J., 1985. "The angle of rotation for plane random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 597-605.
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