Abstract
Words \({a_1a_2\ldots a_n}\) with independent letters a k taken from the set of natural numbers, and a weight (probability) attached via the geometric distribution pq i−1 (p + q = 1) are considered. The parameter \({{\mathcal K}(a_1a_2\ldots a_n)}\) , (the number of weak consecutive records), has proved to be essential in the analysis of a skip list structure. Related to it is the (new) parameter \({{\mathcal M}}\) , i.e., the largest consecutive record in a random word of length n. Exact and asymptotic formulæ are derived for the expectation and the variance.
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Oliver, K., Prodinger, H. Consecutive records in geometrically distributed words. Afr. Mat. 23, 163–172 (2012). https://doi.org/10.1007/s13370-011-0027-9
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DOI: https://doi.org/10.1007/s13370-011-0027-9