Ascending runs of sequences of geometrically distributed random variables: A probabilistic analysis
type: Item
instance of: scholarly article
title: Ascending runs of sequences of geometrically distributed random variables: A probabilistic analysis
zbMATH Open document ID: 1023.60060
DOI: 10.1016/S0304-3975(03)00051-3
author: Guy Louchard
author: Helmut Prodinger
published in: Theoretical Computer Science
publication date: 2003-08-17T00:00:00Z
review text: The authors consider geometrically distributed random variables (RVs), sequences obtained by such independent RVs, and ascending runs (i.e. continuously increasing sequences) on the invoked sequences. The aim of this paper is to study several asymptotic properties of the sequences of ascending runs of geometrically distributed RVs. The paper comprises the combinatorial structure of polyomino, a set of points made up of integer pairs such that every point can be reached from another by a sequence of steps in the lattice plane (up to translation). Using a description of the ascending runs either as a (Markov chain) stochastic process or as a polyomino, the authors derive several new asymptotic probability distributions of RVs and processes such as asymptotic Markov chain and limiting trajectories, number of runs and run length distribution, hitting time to a length \(k\) run and maximum run length. The obtained results are mainly based on the \(q\)-series theoretical framework.
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 1965390
zbMATH Keywords: geometrically distributed random variables
zbMATH Keywords: ascending runs of random variables
zbMATH Keywords: asymptotic properties
zbMATH Keywords: polyomino combinatorial structure
zbMATH Keywords: asymptotic Markov chain
zbMATH Keywords: limiting trajectories
reviewed by: Neculai Curteanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1965390