Related papers: Normalized image of a vector by an infinite produc…
In this paper we give an example of uniform convergence of the sequence of column vectors $\displaystyle{A_1\dots A_nV\over\left\Vert A_1\dots A_nV\right\Vert}$, $A_i\in\{A,B,C\}$, $A,B,C$ being some $(0,1)$-matrices of order $7$ with much…
We consider the infinite sequences $(A\_n)\_{n\in\NN}$ of $2\times2$ matrices with nonnegative entries, where the $A\_n$ are taken in a finite set of matrices. Given a vector $V=\pmatrix{v\_1\cr v\_2}$ with $v\_1,v\_2>0$, we give a…
A sofic measure is the image of a Markov probability measure by a continuous morphism, and can be represented by means of products of matrices $A_n$ that belong to a finite set of nonnegative matrices. To prove that the multifractal…
We study the ergodic properties of a class of measures on $\Sigma^{\mathbb{Z}}$ for which $\mu_{\mathcal{A},t}[x_{0}\cdots x_{n-1}]\approx e^{-nP}\left \|A_{x_{0}}\cdots A_{x_{n-1}}\right \| ^{t}$, where $\mathcal{A}=(A_{0}, \ldots ,…
This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear…
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…
We present a multidimensional generalization of Zeckendorf's Theorem (any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers) to a large family of linear recurrences. This extends work of Anderson and…
We study the selfsimilarity and the Gibbs properties of several measures defined on the product space $\Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}$. This space can be identified with the interval $[0,1]$ by means of the numeration in base…
A random vector ${\bf X}$ is weakly stable iff for all $a,b \in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X} + b {\bf X}' \stackrel{d}{=} {\bf X} \Theta$, where $X'$ is an independent copy of $X$ and $\Theta$ is…
We generalize the Beckner's type Poincar\'e inequality \cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\mu\star\nu$, where $\mu$ is the reference Gaussian measure and $\nu$ is a probability…
By Zeckendorf's Theorem, every positive integer is uniquely written as a sum of non-adjacent terms of the Fibonacci sequence, and its converse states that if a sequence in the positive integers has this property, it must be the Fibonacci…
We consider the correlations of invariant observables for the $O(N)$ and $\mathbb{C}\mathbb{P}^{N-1}$ models at zero coupling, namely, with respect to the natural group-invariant measure. In the limit where one takes a large power of the…
We analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a…
We introduce a weak formulation of the non-parametric prescribed mean curvature equation with measure data and show the existence and several properties of $BV$ solutions under natural assumptions on the prescribed measure. Our approach…
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
Some integration techniques for real-valued functions with respect to vector measures with values in Banach spaces (and viceversa) are investigated in order to establish abstract versions of classical theorems of Probability and Stochastic…
A theorem of Siebert asserts that if a sequence of semigroups of probability measures on a Lie group G is weakly convergent to a semigroup of the same type, then the corresponding generating functionals are convergent in the weak operator…
We study the combinatorial and algebraic properties of Nonnegative Matrices. Our results are divided into three different categories. 1. We show a quantitative generalization of the 100 year-old Perron-Frobenius theorem, a fundamental…