Bjornberg, Jakob E., Mailler, Cecile ORCID: 0000-0002-0910-8320, Moerters, Peter and Ueltschi, Daniel (2020). Characterising random partitions by random colouring. Electron. Commun. Probab., 25. SEATTLE: UNIV WASHINGTON, DEPT MATHEMATICS. ISSN 1083-589X
Full text not available from this repository.Abstract
Let (X-1, X-2, ...) be a random partition of the unit interval [0, 1], i.e. X-i >= 0 and Sigma(i >= 1) X-i = 1, and let (epsilon(1), epsilon(2), ...) be i.i.d. Bernoulli random variables of parameter p is an element of (0, 1). The Bernoulli convolution of the partition is the random variable Z = Sigma(i >= 1) epsilon X-i(i). The question addressed in this article is: Knowing the distribution of Z for some fixed p is an element of (0, 1), what can we infer about the random partition (X-1, X-2, ...)? 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 1/2.
Item Type: | Journal Article | ||||||||||||||||||||
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URN: | urn:nbn:de:hbz:38-351635 | ||||||||||||||||||||
DOI: | 10.1214/19-ECP283 | ||||||||||||||||||||
Journal or Publication Title: | Electron. Commun. Probab. | ||||||||||||||||||||
Volume: | 25 | ||||||||||||||||||||
Date: | 2020 | ||||||||||||||||||||
Publisher: | UNIV WASHINGTON, DEPT MATHEMATICS | ||||||||||||||||||||
Place of Publication: | SEATTLE | ||||||||||||||||||||
ISSN: | 1083-589X | ||||||||||||||||||||
Language: | English | ||||||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||||||
Subjects: | no entry | ||||||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/35163 |
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