Renormalization flow for extreme value statistics of random variables raised to a varying power

Details Renormalization flow for extreme value statistics of random variables raised to a varying power Renormalization flow for extreme value statistics of random variables raised to a varying power

2011-12-13

arxiv.org/abs/1112.2965v2

J. Phys. A: Math. Theor. 45 115004 (2012)

Physics

Condensed Matter

Statistical Mechanics

21 pages, 1 figure,final version, to appear in Journal of Physics A

Scientific paper

10.1088/1751-8113/45/11/115004

Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n. Under these conditions, a non-standard class of max-stable limit distributions, which mirror the classical ones, emerges. Furthermore a transition mechanism between the classical and the non-standard limit distributions is brought to light. If q(n) grows slower than a characteristic function q*(n), the standard limit distributions are recovered, while if q(n) behaves asymptotically as k.q*(n), non-standard limit distributions emerge.

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