Characterising random partitions by random colouring
| Autor: | Cécile Mailler, Daniel Ueltschi, Jakob E. Björnberg, Peter Mörters |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
residual allocation Probability (math.PR) 010102 general mathematics 01 natural sciences Convolution Combinatorics 010104 statistics & probability Bernoulli's principle Distribution (mathematics) 60K35 FOS: Mathematics Partition (number theory) 60G57 0101 mathematics Statistics Probability and Uncertainty partition structures 60E10 Random variable Mathematics - Probability Unit interval Mathematics |
| Zdroj: | Björnberg, J, Mailler, C, Mörters, P & Ueltschi, D 2020, ' Characterising random partitions by random colouring ', Electronic Communications in Probability, vol. 25, 4 . https://doi.org/10.1214/19-ECP283 Electron. Commun. Probab. |
| Popis: | Let $(X_1,X_2,...)$ be a random partition of the unit interval $[0,1]$, i.e. $X_i\geq0$ and $\sum_{i\geq1} X_i=1$, and let $(\varepsilon_1,\varepsilon_2,...)$ be i.i.d. Bernoulli random variables of parameter $p \in (0,1)$. The Bernoulli convolution of the partition is the random variable $Z =\sum_{i\geq1} \varepsilon_i X_i$. The question addressed in this article is: Knowing the distribution of $Z$ for some fixed $p\in(0,1)$, what can we infer about the random partition? 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 $1/2$. Comment: 12 pages |
| Databáze: | OpenAIRE |
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