In this work we show that the number of horizontal steps in a Motzkin word of length n, drawn at random under uniform distribution, has a Gaussian limit distribution. We also prove a local limit property for the same random variable which stresses its periodic behaviour. Similar results are obtained for the number of peaks in a word of given length drawn at random from the same language.
Frequency of pattern occurrences in Motzkind words / M. Goldwurm, J. GUY PENAUD, N. Saheb. - Bordeaux : Université Bordeaux I, 2005.
Frequency of pattern occurrences in Motzkind words
M. Goldwurm;
2005
Abstract
In this work we show that the number of horizontal steps in a Motzkin word of length n, drawn at random under uniform distribution, has a Gaussian limit distribution. We also prove a local limit property for the same random variable which stresses its periodic behaviour. Similar results are obtained for the number of peaks in a word of given length drawn at random from the same language.
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