Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on random permutations and extreme value distributions

Pavle Mladenovi\'{c}

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Let $\Omega_n$ be the set of all permutations of the set $N_n = \{1, 2, \dots, n\}$ and let us suppose that each permutation $\omega = (a_1, \dots, a_n) \in \Omega_n$ has probability $1/n!$. For $\omega = (a_1, \dots, a_n)$ let $X_{nj} = |a_j - a_{j+1}|$, $j \in N_n$, $a_{n+1} = a_1$, $M_n = \max\{X_{n1}, \dots, X_{nn}\}$. We prove herein that the random variable $M_n$ has asymptotically the Weibull distribution, and give some remarks on the domains of attraction of the Fréchet and Weibull extreme value distributions.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 8 (2002), 157-160.

First available in Project Euclid: 23 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 05A05: Permutations, words, matrices

Random permutations maximum of random sequence Leadbetter's mixing condition extreme value distributions domains of attraction


Mladenovi\'{c}, Pavle. A note on random permutations and extreme value distributions. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 8, 157--160. doi:10.3792/pjaa.78.157.

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