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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A discrete fractal in $ {\bf Z}\sp 1\sb +$


Author: Davar Khoshnevisan
Journal: Proc. Amer. Math. Soc. 120 (1994), 577-584
MSC: Primary 60J15; Secondary 28A80
MathSciNet review: 1185269
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Abstract: In this paper, we show that the level sets of mean zero finite variance random walks in $ {\mathbb{R}^1}$ form a discrete fractal in the sense of Barlow and Taylor. Analogously to the Brownian motion result, the Hausdorff dimension of the level sets is almost surely equal to $ \tfrac{1} {2}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1185269-8
PII: S 0002-9939(1994)1185269-8
Keywords: Discrete fractals, random walks
Article copyright: © Copyright 1994 American Mathematical Society