Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis

Authors:
Guy Louchard;Helmut Prodinger
Affiliations:
Lab. d'Informatique Théorique, Faculté des Sciences, Département d'Informatique, Université Libre de Bruxelles, CP 212, Boulevard du Triomphe, B-1050 Bruxelles, Belgium;The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, P.O. Wits, 2050 Johannesburg, South Africa
Venue:
Theoretical Computer Science
Year:
2003

Citing 12
Cited 2

Approximate counting: a detailed analysis

BIT - Ellis Horwood series in artificial intelligence
Real and complex analysis, 3rd ed.

Real and complex analysis, 3rd ed.
General combinatorial schemas: Gaussian limit distributions and exponential tails

Discrete Mathematics - Special issue on combinatorics and algorithms
Mellin transforms and asymptotics: harmonic sums

Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Probabilistic analysis of some (un)directed animals

Theoretical Computer Science - Special issue: selected papers from “GASCOM '94” and the “Polyominoes and Tilings” workshops
Probabilistic analysis of column-convex and directed diagonally-convex animals

Random Structures & Algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching

The art of computer programming, volume 3: (2nd ed.) sorting and searching
On convergence rates in the central limit theorems for combinatorial structures

European Journal of Combinatorics
Probabilistic analysis of column-convex and directed diagonally-convex animals: II. trajectories and shapes

Random Structures & Algorithms
Runs of geometrically distributed random variables: a probabilistic analysis

Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Combinatorics of Geometrically Distributed Random Variables: Lenght of Ascending Runs

LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Average profile and limiting distribution for a phrase size in the Lempel-Ziv parsing algorithm

IEEE Transactions on Information Theory

Monotone runs of uniformly distributed integer random variables: a probabilistic analysis

Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
The number of distinct values in a geometrically distributed sample

European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures

Quantified Score

Hi-index	5.23

Visualization

Abstract

Using a Markov chain approach and a polyomino-like description, we study some asymptotic properties of sequences of ascending runs of geometrically distributed random variables. We analyze the limiting trajectories, the number of runs and the run length distribution, the hitting time to a length k run and the maximum run length.