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Characterising random partitions by random colouring
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Björnberg, Jakob E., Mailler, Cécile , Mörters, Peter and Ueltschi, Daniel (2020) Characterising random partitions by random colouring. Electronic communications in probability, 25 . pp. 1-12. doi:10.1214/19-ECP283 ISSN 1083-589X.
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Official URL: https://doi.org/10.1214/19-ECP283
Abstract
Let (X1,X2,...) be a random partition of the unit interval [0,1], i.e. Xi
≥0 and ∑i≥1Xi=1, and let (ε1,ε2,...) be i.i.d. Bernoulli random variables of parameter p∈(0,1). The Bernoulli convolution of the partition is the random variable Z=∑i≥1εiXi. The question addressed in this article is: Knowing the distribution of Z for some fixed p∈(0,1), what can we infer about the random partition (X1,X2,...)? We consider random partitions formed by residual allocation and prove that their distributions are fully characterised by their Bernoulli convolution if and only if the parameter
p is not equal to \nicefrac12.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Electronic communications in probability | ||||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||||
ISSN: | 1083-589X | ||||||||
Official Date: | 13 January 2020 | ||||||||
Dates: |
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Volume: | 25 | ||||||||
Page Range: | pp. 1-12 | ||||||||
DOI: | 10.1214/19-ECP283 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 23 July 2019 | ||||||||
Open Access Version: |
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