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 -