The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis.

Guy Louchard, Werner Schachinger, Mark Daniel Ward

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

The analysis of strings of n random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the asymptotic (n → ∞) mean of this number in the cases of different and identical pairs. In this paper we are interested in all asymptotic moments in the identical case, in the asymptotic variance in the different case and in the asymptotic distribution in both cases. We use two approaches: the first one, the probabilistic approach, leads to variances in both cases and to some conjectures on all moments in the identical case and on the distribution in both cases. The second approach, the combinatorial one, relies on multivariate pattern matching techniques, yielding exact formulas for first and second moments. We use such tools as Mellin transforms, Analytic Combinatorics, Markov Chains.

OriginalspracheEnglisch
Aufsatznummer3
Seitenumfang47
FachzeitschriftDiscrete Mathematics and Theoretical Computer Science
Jahrgang25
Ausgabenummer2
DOIs
PublikationsstatusVeröffentlicht - 2023

ÖFOS 2012

  • 101024 Wahrscheinlichkeitstheorie

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