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

Published online by Cambridge University Press:  14 July 2016

Claude Bélisle  and
Julian Faraway
Claude Bélisle
Affiliation:
University of Michigan
Julian Faraway*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA.
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Abstract

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.

Keywords

BROWNIAN MOTIONRANDOM WALK ON INTEGER LATTICE
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 717 - 726
Copyright
Copyright © Applied Probability Trust 1991 

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