Projects per year
Abstract
Let (X1, X2, …) be a random partition of the unit interval [0, 1], i.e. Xi ≥ 0 and ∑i≥1 Xi = 1, and let (ε1, ε2, …) be i.i.d. Bernoulli random variables of parameter p ϵ (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 ϵ (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 to1/2.
Original language  English 

Article number  4 
Journal  Electronic Communications in Probability 
Volume  25 
DOIs  
Publication status  Published  2020 
Fingerprint
Dive into the research topics of 'Characterising random partitions by random colouring'. Together they form a unique fingerprint.Projects
 1 Finished

Fellowship  Random trees: analysis and applications
Engineering and Physical Sciences Research Council
1/06/18 → 31/05/22
Project: Research council