Institut de Mathématiques de Toulouse

Accueil > Événements Scientifiques > Séminaires & Groupes de Travail > Anciens Séminaires > Analyse géométrique et probabilité

Analyse géométrique et probabilité

par Benoît Huou, Raphaël Bouyrie - publié le

  • Jeudi 17 octobre 2013 14:00-15:00 - Elizabeth Meckes - Université de Cleveland

    Projections of probability distributions : A measure-theoretic Dvoretzky theorem.

    Résumé : Dvoretzky’s theorem tells us that if we put an arbitrary norm on n-dimensional Euclidean space, no matter what that normed space is like, if we pass to subspaces of dimension about log(n), the space looks pretty much Euclidean. A related measure-theoretic phenomenon has long been observed : the (one-dimensional) marginals of many natural high-dimensional probability distributions look about Gaussian. A question which had received little attention until recently is whether this phenomenon persists for k-dimensional marginals for k growing with n, and if so, for how large a k ? In this talk I will discuss recent work showing that the phenomenon does indeed persist if k less than 2log(n)/log(log(n)), and that this bound is sharp (even the 2 !).
    The talk will not assume much background and not get too much into the technicalities — we can do that later if people are interested.

    Lieu : Salle de conférence M.I.P. 1R3 - Université Paul Sabatier
    118 route de Narbonne
    31000 Toulouse

  • Jeudi 7 novembre 2013 14:00-15:00 - Witold Bednorz - Warsaw University

    Path properties of Gaussian processes

    Résumé : In the talk there will be described the problem of regularity of paths for general Gaussian processes. The basic property is the sample boundedness, more advanced are continuity and Holder continuity of paths. There will be provided all necessary tools to investigate path properties : Sudakov minoration and Gaussian concentration. The tools will be used to sketch the proof of Talagrand’s theorem that completely characterizes the problem of sample boundedness and continuity of Gaussian processes.

    Lieu : Salle de conférence M.I.P. 1R3

  • Jeudi 14 novembre 2013 14:00-15:00 - Witold Bednorz - Warsaw University

    Bernoulli Theorem

    Résumé : The talk will concern the problem of the sample boundedness of Bernoulli processes. There will be provided all the tools necessary to prove the so called Bernoulli Conjecture and a rough scetch of the proof. Then some applications appear (maximal inequality problem, Fourier series) as well as a list of open problems.

    Lieu : Salle de conférence M.I.P. 1R3

  • Jeudi 21 novembre 2013 14:00-15:00 - Raphaël Bouyrie - Institut de Mathématique de Toulouse

    Discrete proof of "Majority is stablest" theorem, from De-Mossel-Neeman.

    Résumé : The "Majority is Stablest" (MIS) theorem states that the Majority function maximize noise stabiltity among balanced boolean functions on the discrete cube with "small" influences.
    We will present a recent proof, done by De, Mossel and Neeman, of the MIS theorem of Mossel, Oleskiewicz and O’Donnell.

    Lieu : Salle de conférence M.I.P. 1R3

  • Jeudi 28 novembre 2013 14:00-15:00 - Benoit Huou - I.M.T.

    Uniform enlargement and geometric influences

    Lieu : Salle de conférences M.I.P. - bâtiment 1R3 - 1er étage

  • Jeudi 5 décembre 2013 14:00-15:00 - Laurent Miclo - Institut de Mathématiques de Toulouse

    Strong stationary times for one-dimensional diffusions

    Lieu : Salle de conférence MIP

  • Jeudi 12 décembre 2013 14:00-15:00 - Pawel Wolff - Warsaw University

    Generalized Young’s convolution inequalities

    Lieu : Salle de conférence M.I.P.

  • Jeudi 19 décembre 2013 14:00-15:00 - Mark Meckes - Université de Cleveland

    Maximizing entropy and diversity

    Résumé : I will discuss a class of functionals on finite probability spaces, introduced by T. Leinster, which generalize Rényi entropies. I will prove a theorem about maximizing these functionals, and will show how this maximization problem is connected to theoretical ecology, combinatorics, probability, and geometry.

    Lieu : Salle de conférence M.I.P.

  • Jeudi 16 janvier 2014 10:00-11:00 - Jospeh Lehec - Université Paris 9 (Dauphine)

    Thin shell implies spectral gap up to a log

    Lieu : Salle de conférence MIP

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