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Sequential and continuous time stick-breaking

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Arndt,  Peter F.
Evolutionary Genomics (Peter Arndt), Dept. of Computational Molecular Biology (Head: Martin Vingron), Max Planck Institute for Molecular Genetics, Max Planck Society;

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Arndt_2019.pdf
(Publisher version), 553KB

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Citation

Arndt, P. F. (2019). Sequential and continuous time stick-breaking. Journal of Statistical Mechanics: Theory and Experiment, 2019: 064003. doi:10.1088/1742-5468/ab1dd8.


Cite as: http://hdl.handle.net/21.11116/0000-0004-CFDA-E
Abstract
The repeated breaking of a linear object, for example a stick, is a fundamental process which underlies numerous natural phenomena. Here we compare two distinct ensembles of stick-breaking: (i) a stick is broken with a certain rate over time; and (ii) a stick is broken a finite number of times. Both ensembles are deduced from appropriate integral equations and related to each other. The analyses performed here and the comparison of the two ensembles enables us to better understand the stick-breaking process by itself.