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

F. Angeletti, E. Bertin, P. Abry, J. Phys. A, (2012), 115004, ### Abstract

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 $\lambda q^*_n$,non-standard limit distributions emerge.