Daniel Ueltschi

Let (X_1,X_2,...) be a random partition of the unit interval [0,1],
i.e. X_i ≥ 0 and ∑_i X_i = 1, and let (ε_1,ε_2,...) be i.i.d.
Bernoulli random variables of parameter p∈(0,1). The Bernoulli
convolution of the partition is the random variable Z=∑_i ε_i X_i. The
question addressed here is: Knowing the distribution of Z for some
fixed p∈(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.
This is joint work with Jakob Björnberg, Cécile Mailler and Peter Mörters.