Eric Olivier

activity

20042010

most citedHow to prove that some Bernoulli convolution has the weak Gibbs property

2 citations · 4 across the 5 of their papers we have counts for

collaborators

5 papers

math.DS2010★ 2 cited

How to prove that some Bernoulli convolution has the weak Gibbs property

Éric Olivier, Alain Thomas

In this paper we give an example of uniform convergence of the sequence of column vectors $\frac{A _{1} \dots A _{n} V}{∥ A _{1} \dots A _{n} V ∥}$ , $A_{i} \in {A, B, C}$ ,…

math.PR2009★ 1 cited

Projective convergence of columns for inhomogeneous products of matrices with nonnegative entries

Éric Olivier, Alain Thomas

Let $P_{n}$ be the $n$ -step right product $A_{1} \dots A_{n}$ , where $A_{1}, A_{2}, \dots$ is a given infinite sequence of $d \times d$ matrices with nonnegative entries. In a wide range of sit…

math.NT2006

Weak Gibbs property and system of numeration

Eric Olivier, Alain Thomas

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space $Ω\_r:=\{0,1,...,\break r-1\}^{\mathbb N}$. This space can be identified with…

math.NT2006★ 1 cited

Infinite products of $2 \times 2$ matrices and the Gibbs properties of Bernoulli convolutions

Eric Olivier, Alain Thomas

We consider the infinite sequences $(A\_n)\_{n\in\NN}$ of $2 \times 2$ matrices with nonnegative entries, where the $A_n$ are taken in a finite set of matrices. Given a vector $V=\p…

math.NT2004

On the Gibbs properties of Bernoulli convolutions related to $β$ -numeration in multinacci bases

Eric Olivier, Nikita Sidorov, Alain Thomas

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $β$ -numeration. A matrix decomposition of these measures is obtained in the ca…