Alain Thomas

activity

20042013

most citedCan an infinite left-product of nonnegative matrices be expressed in terms of infinite left-products of stochastic ones?

3 citations · 7 across the 8 of their papers we have counts for

collaborators

9 papers

math.DS2013

Sofic measures and densities of level sets

Alain Thomas

The Bernoulli convolution associated to the real $β > 1$ and the probability vector $(p_{0}, .., p_{d - 1})$ is a probability measure $η_{β, p}$ on $R$ , solution of the self-similar…

math.PR2013

Almost sure convergence of products of $2 \times 2$ nonnegative matrices

Alain Thomas

We study the almost sure convergence of the normalized columns in an infinite product of nonnegative matrices, and the almost sure rank one property of its limit points. Given a pr…

math.RA2010

Infinite products of nonnegative $2 \times 2$ matrices by nonnegative vectors

Alain Thomas

Given a finite set ${M_{0}, \dots, M_{d - 1}}$ of nonnegative $2 \times 2$ matrices and a nonnegative column-vector $V$ , we associate to each $(ω_{n}) \in {0, \dots, d - 1}^{N}$ the seq…

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.PR2009★ 3 cited

Can an infinite left-product of nonnegative matrices be expressed in terms of infinite left-products of stochastic ones?

Alain Thomas

If a left-product $M_{n} ... M_{1}$ of square complex matrices converges to a nonnull limit when $n \to \infty$ and if the $M_{n}$ belong to a finite set, it is clear that there exists an i…

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…

Sofic measures and densities of level sets

Almost sure convergence of products of 2×2 nonnegative matrices

Infinite products of nonnegative 2×2 matrices by nonnegative vectors

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

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

Can an infinite left-product of nonnegative matrices be expressed in terms of infinite left-products of stochastic ones?

Weak Gibbs property and system of numeration

Infinite products of 2×2 matrices and the Gibbs properties of Bernoulli convolutions

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

Almost sure convergence of products of $2 \times 2$ nonnegative matrices

Infinite products of nonnegative $2 \times 2$ matrices by nonnegative vectors

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

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