Approximate counting: a detailed analysis
BIT - Ellis Horwood series in artificial intelligence
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
Random Structures & Algorithms
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Distinctness of compositions of an integer: a probabilistic analysis
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Concrete Math
Runs of geometrically distributed random variables: a probabilistic analysis
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis
Theoretical Computer Science
Average profile and limiting distribution for a phrase size in the Lempel-Ziv parsing algorithm
IEEE Transactions on Information Theory
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Using a Markov chain approach and a polyomino-like description, we study some asymptotic properties of monotone increasing runs of uniformly distributed integer random variables. We analyze the limiting trajectories, which after suitable normalization, lead to a Brownian motion, the number of runs, which is asymptotically Gaussian, the run length distribution, the hitting time to a large length k run, which is asymptotically exponential, and the maximum run length which is related to the Gumbel extreme-value distribution function. A preliminary application to DNA analysis is also given.