Related papers: Independence of multipliers in several variables c…
Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large…
We show that the set of complex points in the moduli space of polynomials of degree d corresponding to post-critically finite polynomials is a set of algebraic points of bounded height. It follows that for any B, the set of conjugacy…
A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable…
The multiplier $\lambda_n$ of a periodic orbit of period $n$ can be viewed as a (multiple-valued) algebraic function on the space of all complex quadratic polynomials $p_c(z)=z^2+c$. We provide a numerical algorithm for computing critical…
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the…
Let $F$ be a polynomial endomorphism of $\C^n$ which extends holomorphically to $\P^n$. We prove that the dimension of $\mu_F$, the pluriharmonic measure on the boundary of the filled Julia set of $F$, is bounded above by $2n-1$.
[PhD thesis of FCP.] Nowadays, genetics studies large amounts of very diverse variables. Mathematical statistics has evolved in parallel to its applications, with much recent interest high-dimensional settings. In the genetics of human…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…
We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…
Let $V$ be an infinite-dimensional vector space over a field. In a previous article, we have shown that every endomorphism of $V$ splits into the sum of four square-zero ones but also into the sum of four idempotent ones. Here, we study…
We consider families of geometries of D--dimensional space, described by a finite number of parameters. Starting from the De Witt metric we extract a unique integration measure which turns out to be a geometric invariant, i.e. independent…
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…
We prove that the Cayley-Menger determinant of an $n$-dimensional simplex is an absolutely irreducible polynomial for $n\geq3.$ We also study the irreducibility of polynomials associated to related geometric constructions.
In this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of fixed degree, or within a fixed number field, and bounded height.
On a Riemannian compact manifold, we give existence and multiplicity results for solutions of elliptic PDE by introducing isometry invariances. When the groups we used have finite orbits, we get multiplicity results for equations with the…
The number of functionally independent scalar invariants of arbitrary order of a generic pseudo--Riemannian metric on an $n$--dimensional manifold is determined.
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most…
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…
We prove that Brinkmann's problems are decidable for endomorphisms of $F_n\times F_m$: given $(x,y),(z,w)\in F_n\times F_m$ and $\Phi\in \text{End}(F_n\times F_m)$, it is decidable whether there is some $k\in \mathbb{N}$ such that…