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1 results

  • Winding angle and maximum winding angle of the two-dimensional random walk

  • Claude Bélisle, Julian Faraway
  • Journal:
    Journal of Applied Probability / Volume 28 / Issue 4 / December 1991
    Published online by Cambridge University Press:
    14 July 2016, pp. 717-726
    Print publication:
    December 1991

  • Recent results on the winding angle of the ordinary two-dimensional random walk on the integer lattice are reviewed. The difference between the Brownian motion winding angle and the random walk winding angle is discussed. Other functionals of the random walk, such as the maximum winding angle, are also considered and new results on their asymptotic behavior, as the number of steps increases, are presented. Results of computer simulations are presented, indicating how well the asymptotic distributions fit the exact distributions for random walks with 10m steps, for m = 2, 3, 4, 5, 6, 7.