Asymptotic Normality for Oscillation of Permutation
Chern-Ching Chao, Zhidong Bai, Wen-Qi Liang · Probability in the Engineering and Informational Sciences · 1993
Suppose each permutation (πl,…,πn) of ( 1, …,n) has probability 1/n!. The oscillation of (πl; …, πn) is defined asTn= | πk− πk+1|, where πn+1= π1. It is proved that (Tn−ETn)/(varTn)1/2converges in distribution toN(0,1). The connection between the oscillation and the presortedness measure is also discussed.