Correlations between record events in sequences of random variables with a linear trend

Details Correlations between record events in sequences of random variables with a linear trend Correlations between record events in sequences of random variables with a linear trend

2011-05-19

arxiv.org/abs/1105.3915v3

Journal of Statistical Physics 144 (2011) 1206-1222

Physics

Condensed Matter

Statistical Mechanics

19 pages, 12 figures; some typos in Sections 3.1 and 3.3. corrected

Scientific paper

10.1007/s10955-011-0307-7

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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