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- W2039603000 abstract "A self-modifying random walk on ${Bbb Q}$ is derived from an ordinary random walk on the integers by interpolating a new vertex into each edge as it is crossed. This process converges almost surely to a random variable which is totally singular with respect to Lebesgue measure, and which is supported on a subset of ${Bbb R}$ having Hausdorff dimension less than $1$ , which we calculate by a theorem of Billingsley. By generating function techniques we then calculate the exponential rate of convergence of the process to its limit point, which may be taken as a bound for the convergence of the measure in the Wasserstein metric. We describe how the process may viewed as a random walk on the space of monotone piecewise linear functions, where moves are taken by successive compositions with a randomly chosen such function." @default.
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- W2039603000 date "1997-01-17" @default.
- W2039603000 modified "2023-09-23" @default.
- W2039603000 title "Zeno's walk: A random walk with refinements" @default.
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- W2039603000 doi "https://doi.org/10.1007/s004400050078" @default.
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