Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Morpho-statistical description of networks through graph modelling and Bayesian inference

Abstract: Collaboration graphs are relevant sources of information to understand behavioural tendencies of groups of individuals. The study of these collaboration graphs enables figuring out factors that may affect the efficiency and the sustainability of cooperative work. An example of such a collaboration involves researchers who develop relationships with their external counterparts to tackle scientific challenges. We propose a statistical approach that considers edge occurrence in the graph as a labelling process. Our approach combines spatial processes modelling and Exponential Random Graph Models (ERGMs) commonly used to analyse such social processes. Since the normalising constant involved in classical Markov Chain Monte Carlo approaches is not available in an analytic closed form, the inference remains challenging. To overcome this issue, we propose a Bayesian tool that relies on the recent ABC Shadow algorithm. The proposed method is illustrated on real data sets from an open archive of scholarly documents.

Strong solutions to stochastic differential equations with rough coefficients

Abstract: We study strong existence and pathwise uniqueness for stochastic differential equations in $\RR^d$ with rough coefficients, and without assuming uniform ellipticity for the diffusion matrix. Our approach relies on direct quantitative estimates on solutions to the SDE, assuming Sobolev bounds on the drift and diffusion coefficients, and $L^p$ bounds for the solution of the corresponding Fokker-Planck PDE, which can be proved separately. This allows a great flexibility regarding the method employed to obtain these last bounds. Hence we are able to obtain general criteria in various cases, including the uniformly elliptic case in any dimension, the one-dimensional case and the Langevin (kinetic) case.

Propriétés multiplicatives d'entiers soumis à des conditions digitales

Abstract: Pour une base fixee, les entiers ellipsephiques (c'est-a-dire les entiers dont l'ecriture n'utilise que certains chiffres) et les palindromes forment des sous ensembles eparses des entiers, ensembles definis par des conditions digitales. Nous etudions si ces ensembles ont des proprietes multiplicatives similaires a celles des entiers. Nous evaluons d'abord les grands moments de la serie generatrice des entiers ellipsephiques. Comme application, nous en deduisons l'existence d'un 0 Nous etablissons ensuite un resultat de crible ou les modules possedant un nombre anormalement grand de diviseurs sont ecartes du terme d'erreur. Nous en deduisons l'existence d'une proportion positive d'entiers ellipsephiques friables c'est-a-dire possedant tous leurs facteurs premiers majores par n^c, pour une constante c Nous montrons enfin a l'aide de techniques elementaires comment reduire l'etude de la serie generatrice des palindromes a une serie proche de celle des entiers ellipsephiques ce qui permet d'etudier la repartition des palindromes dans les progressions arithmetiques et ainsi d'obtenir une majoration de l'ordre de grandeur attendu du nombre de palindromes premiers. Nous en deduisons en particulier l'existence d'une infinite de palindromes possedant en base 10 au plus 372 facteurs premiers (comptes avec multiplicite).

Spectral Theory near Thresholds for Weak Interactions with Massive Particles

Abstract: We consider a Hamiltonian describing the weak decay of the massive vector boson Z0 into electrons and positrons. We show that the spectrum of the Hamiltonian is composed of a unique isolated ground state and a semi-axis of essential spectrum. Using a suitable extension of Mourre's theory, we prove that the essential spectrum below the boson mass is purely absolutely continuous.