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arXiv · 1206.4432

Rounding Effects in Record Statistics

G. Wergen·D. Volovik·S. Redner·J. Krug
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Abstract

We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding down to integer multiples of a discretization scale $Δ>0$. Rounding leads to ties of an existing record, thereby reducing the number of new records. For an infinite number of random variables that are drawn from distributions with a finite upper limit, the number of discrete records is finite, while for distributions with a thinner than exponential upper tail, fewer discrete records arise compared to continuous variables. In the latter case the record sequence becomes highly regular at long times.

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G. Wergen, D. Volovik, S. Redner, J. Krug. 2012-10-22. Rounding Effects in Record Statistics. https://doi.org/10.1103/physrevlett.109.164102

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