TY - JOUR

T1 - Characterising random partitions by random colouring

AU - Björnberg, Jakob

AU - Mailler, Cecile

AU - Mörters, Peter

AU - Ueltschi, Daniel

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

U2 - 10.1214/19-ECP283

DO - 10.1214/19-ECP283

M3 - Article

VL - 25

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

M1 - 4

ER -