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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, June 12, 2018}
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\textbf{At} \emph{11:00 -- 12:00}
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\textbf{In} \emph{201}

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{\large\scshape Yotam Smilansky}
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will talk about
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{\Large\bfseries Kakutani's splitting procedure for multiscale substitution schemes\par}
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\textsc{Abstract:}
In 1975, S. Kakutani introduced a splitting procedure which generates a sequence of partitions of the unit interval {[}0,1{]}, and showed that this sequence is uniformly distributed in {[}0,1{]}. We present generalizations of this procedure in higher dimensions, which correspond to constructions used when defining substitution and multiscale substitution tilings of Euclidean space. We prove uniform distribution of these sequences of partitions using new path counting results on graphs and establish Kakutani's result as a special case.








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