Martingales et grandes déviations pour les arbres binaires de recherche

We establish almost sure and in mean large deviations theorems for the leaf structure of binary search trees (b.s.t.). To this end, a parameterized family of martingales is introduced. This family also allows us to have asymptotic results on the number of final leaves of a b.s.t.     

Dimension de la mesure d’équilibre d’applications méromorphes

The Journal of Geometric Analysis - Let ? be a dominating meromorphic self-map of a compact Kähler manifold. Assume that the topological degree of ? is larger than the other...     

Les coefficients cinematiques d’élasticité

Annali di Matematica Pura ed Applicata (1923 -) - L’auteur propose de modifier la loi deHooke de façon à exprimer le travail élastique en function de l’unité de...     

Actions affines sur les arbres réels

Résumé. Nous commencons par une étude générale des actions affines sur les arbres réels. Nous prouvons que, sauf cas dégénérés, l'action par isométries du sous-groupe des commutateurs détermine l'action affine du groupe total. Ensuite, nous exhibons des actions affines libres de groupes qui ne peuvent agir librement par isométries sur les arbres réels.

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We first study affine actions on real trees in general; we show that, except for some degenerate cases, the isometric action of the commutators group determines the affine action of the whole group. We then give examples of free affine actions of groups which cannot act freely and isometrically on real trees.

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Received: 11 November 1998; in final form: 22 February 2000 / Published online: 25 June 2001     

Existence d’immeubles triangulaires quasi-périodiques

On s’intéresse à la structure dynamique de l’espace E des immeubles triangulaires et on montre en particulier:

Dégénérescence de séries d’Eisenstein hyperboliques

In this work, we deal with hyperbolic Eisenstein series and more particularly, given a degenerating family S _l (l ≥ 0) of Riemann Surfaces with their canonical hyperbolic metrics, we work out the degeneration of hyperbolic Eisenstein series associated to the pinching geodesics in S _l . Our principal results are theorems 2.2, 4.1 et 4.2.     

Désingularisation de métriques d’Einstein. I

We find a new obstruction for a real Einstein 4-orbifold with an A ₁-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with boundary at infinity a conformal metric, we prove that if the obstruction vanishes, one can desingularize Einstein orbifolds with such singularities. The Dirichlet problem consists in finding Einstein metrics with given conformal infinity on the boundary: we prove that our obstruction defines a wall in the space of conformal metrics on the boundary, and that all the Einstein metrics must have their conformal infinity on one side of the wall.     

Inégalité d’Ahlfors en dimension supérieure

We prove an Ahlfors’ like inequality for the holomorphic curves with boundary of a complex compact Kobayashi-hyperbolic manifold.     

Estimation d’intégrales de processus multi-fractionnaires

In this Note, we consider the problem of predicting integrals of multi-fractional stochastic processes. We prove that the mean square error is asymptotically dominated by the infimum of the fractional index, and that there is no asymptotically optimal sampling design. Our result extend Stein's uni-fractional results to the multi-fractional framework.     

Construction d’entrelacs hyperpoliques et arithmétiques

In this Note, we continue the study started in [4] about arithmetic hyperbolic links L such that S³\L is homeomorphic to H³/Γ, where Γ is not conjugate to a subgroup of any Bianchi group. One describes the steps of the construction, different from the construction in [4], which permits us to determine the first known examples in M₂(Q (i√39)) and M₂(Q (i√6 respectively.     

Généralisation d’un théorème de Greenberg

We formulate a general conjecture on the characteristic polynomials of S-decomposed T-ramified Iwasawa modules over the cyclotomic \(\mathbb {Z}_\ell \)-extension of a number field. We show that this conjecture is equivalent to the conjunctions of the classical conjectures of Leopoldt and of Gross-Kuz’min. We so extend a result of semi-simplicity of Greenberg and, by the way, an isomorphism of Kuz’min.     

Suites d’Applications Méromorphes Multivaluées et Courants Laminaires

Let F_n: X₁ → X₂ be a sequence of (multivalued) meromorphic maps between compact Kähler manifolds. We study the asymptotic distribution of preimages of points by F_n and, for multivalued self-maps of a compact Riemann surface, the asymptotic distribution of repelling fixed points. Let (Z_n) be a sequence of holomorphic images of ?^s in a projective manifold. We prove that the currents, defined by integration on Z_n, properly normalized, converge to currents which satisfy some laminarity property. We also show this laminarity property for the Green currents, of suitable bidimensions, associated to a regular polynomial automorphism of ?^k or an automorphism of a projective manifold.     

Comment détecter le délit d'initiés?

This Note uses the enlargement of filiations for modelling the observation of a financial market by an insider trader. A characterization of admissible strategies and a criterium for optimization are given. Then a statistical test is proposed to test the unknown of the future against its knowledge.     

Nouvelle démonstration d’un théorème de P. A. Smith

Sans résumé A Monsieur H. Hopf, à l’occasion de son soixantième anniversaire