Characterising random partitions by random colouring
Journal article, 2020

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.

residual allocation

partition structures


Jakob Björnberg

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Cecile Mailler

University of Bath

Peter Moerters

University of Cologne

Daniel Ueltschi

The University of Warwick

Electronic Communications in Probability

1083-589X (ISSN)

Vol. 25 4

Subject Categories


Probability Theory and Statistics

Discrete Mathematics



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