Some stochastic processes in a random permutation
type: Item
instance of: scholarly article
title: Some stochastic processes in a random permutation
zbMATH Open document ID: 0648.60027
DOI: 10.1016/0378-3758(88)90075-4
author: A. J. Stam
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
review text: For a random permutation \(\sigma\) of \(\{\) 1,2,...,N\(\}\), an increasing success at i is the event that \(\sigma (i)=j\), \(\sigma (k)=j-1\) for some \(k<i\) and \(j\geq 2\), and a decreasing success the event that \(\sigma (i)=h\), \(\sigma (k)=h+1\) for some \(k<i\) and \(h\leq N-1\). Three processes of events which have the same distribution are considered. The first of them is defined in terms of rises and descents of \(\sigma\), the second one on a random circular permutation of \(\{1,2,...,N+1\}\) and the third one on a chess board model. Next, the distributions of some statistics of these processes are given and their asymptotic behaviour as \(N\to \infty\) is studied.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 4058524
zbMATH Keywords: random permutation
zbMATH Keywords: random circular permutation
zbMATH Keywords: chess board model
zbMATH Keywords: asymptotic behaviour
MaRDI profile type: Publication
full work available at URL: 0378-3758(88)90075-4
OpenAlex ID: W1986100039
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description: scientific article; zbMATH DE number 4058524