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International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité proche de 1, la plupart des valeurs propres sont proches d’un cercle.Nous étudions la répartitions moyenne des valeurs propres à l’intérieur de ce cercle et nous en donnons une description asymptotique précise.

International audience; Abstract This paper proposes a reconsideration of mathematical structuralism, inaugurated by Bourbaki, by adopting the “practical turn” that owes much to Henri Poincare. By reconstructing his group theoretic approach of geometry, it seems possible to explain the main difficulty of modern philosophical eliminative and non-eliminative structuralism: the unclear ontological status of ‘structures’ and ‘places’. The formation of the group concept—a ‘universal’—is suggested by a specific system of stipulated sensations and, read as a relational set, the general group concept constitutes a model of the group axioms, which are exemplified (in the Goodmanian sense) by the sensation system. In other words, the shape created in the mind leads to a particular type of platonistic universals, which is a model (in the model theoretical sense) of the mathematical axiom system of the displacement group. The elements of the displacement group are independent and complete entities with respect to the axiom system of the group. But, by analyzing the subgroups of the displacement group (common to geometries with constant curvature) one transforms the variables of the axiom system in ‘places’ whose ‘objects’ lack any ontological commitment except with respect to the specified axioms. In general, a structure R is interpreted as a second order relation, which is exemplified by a system of axioms according to the pragmatic maxim of Peirce.