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Correlations Between Record Events in Sequences of Random Variables with a Linear Trend

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An Erratum to this article was published on 21 October 2011

Abstract

The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics beyond the case of i.i.d. random variables have received much attention, but the question of independence of record events has not been addressed systematically. In this paper, we study this question in detail for the case of independent, non-identically distributed random variables, specifically, for random variables with a linearly moving mean. We find a rich pattern of positive and negative correlations, and show how their asymptotics is determined by the universality classes of extreme value statistics.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, Cologne, Germany

    Gregor Wergen, Jasper Franke & Joachim Krug

Authors
  1. Gregor Wergen
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  2. Jasper Franke
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  3. Joachim Krug
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Correspondence to Joachim Krug.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10955-011-0376-7

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Wergen, G., Franke, J. & Krug, J. Correlations Between Record Events in Sequences of Random Variables with a Linear Trend. J Stat Phys 144, 1206 (2011). https://doi.org/10.1007/s10955-011-0307-7

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