On the Variety of Shapes in Digital Trees

Jeffrey Gaither (), Hosam Mahmoud () and Mark Daniel Ward ()
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Jeffrey Gaither: The Ohio State University
Hosam Mahmoud: The George Washington University
Mark Daniel Ward: Purdue University

Journal of Theoretical Probability, 2017, vol. 30, issue 4, 1225-1254

Abstract: Abstract We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we be very explicit about the specification of the underlying measure-theoretic formulation. We show that (under appropriate normalization) for such a collection, any linear combination of the number of occurrences of each of the motifs in the data has a limiting normal distribution. In many instances, this can be interpreted in terms of the number of occurrences of individual motifs: They have a multivariate normal distribution. The methods of proof include combinatorics on words, integral transforms, and poissonization.

Keywords: Analysis of algorithms; Random trees; Digital trees; Recurrence; Functional equation; Mellin transform; Poissonization; Digital data; Combinatorics on words; Similarity of strings; Motif; Primary: 05C05; 60C05; Secondary: 68P05; 68P10; 68P20 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0700-x

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