Density of near-extreme events

Details Density of near-extreme events Density of near-extreme events

2007-01-16

arxiv.org/abs/cond-mat/0701375v2

Phys. Rev. Lett. vol. 98, pp. 140201 (2007)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, revtex4. Minor corrections, references updated. This is slightly extended version of the Published one (Ph

Scientific paper

10.1103/PhysRevLett.98.140201

We provide a quantitative analysis of the phenomenon of crowding of near-extreme events by computing exactly the density of states (DOS) near the maximum of a set of independent and identically distributed random variables. We show that the mean DOS converges to three different limiting forms depending on whether the tail of the distribution of the random variables decays slower than, faster than, or as a pure exponential function. We argue that some of these results would remain valid even for certain {\em correlated} cases and verify it for power-law correlated stationary Gaussian sequences. Satisfactory agreement is found between the near-maximum crowding in the summer temperature reconstruction data of western Siberia and the theoretical prediction.

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