Asymptotic behavior of permutation records

Asymptotic behavior of permutation records

Article history: Received 14 June 2008 Available online 8 April 2009

Asymptotic Normality of Statistics on Permutation Tableaux

Abstract. In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic statistics (like the number of unrestricted rows, the number of rows, and the number of 1s in the first row) exactly. In all three cases the distribution...

Asymptotic probability distributions of some permutation statistics

We present in this work results on some distributions of permutation statistics of random elements of the wreath product Gr,n = Cr ! Sn. We consider the distribution of the descent number, the flag major index, the excedance, and the number of fixed points, over the whole group Gr,n or over the subclasses of derangements and involutions. We compute the mean, variance and moment generating funct...

On the asymptotic theory of permutation statistics

In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned on the σ-field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general contiguous alternatives with independent but not identically distributed observations. The proofs are...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions