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Rounding effects in record statistics
G Wergen1, D Volovik, S Redner
1Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany.
Abstract:
We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding 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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