A partir de la rentrée 2013, le langage Python (avec ses bibliothèques Numpy, Scipy et matplotlib) devient le langage de référence pour le programme de la matière informatique pour tous en CPGE scientifique (MPSI-PCSI-PTSI-TSI-TPC-TPT). A mon humble avis, le plus simple est d’installer le programme SAGE qui comporte toutes ces bibliothèques intégrées plus une interface Web…
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Edgeworth series refine the central limit theorem. Playing with Stein method and Malliavin calculus, we can retrieve Edgeworth series and precise the error bounds. http://hal.archives-ouvertes.fr/hal-00685272 The infinite dimension version is under preparation.
NEWS : Correction de l’examen 2016 Dans le cadre du Master Parisien de Recherche Opérationnelle, je m’occupe du module de “files d’attente”. Vous trouverez ici les documents associés. Le livre “Modélisation et analyse stochastique des réseaux des télécommunications” est publié chez Hermès depuis novembre 2011. Vous pouvez l’acheter avec 30% de réduction. Transparents Chaînes de…
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We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an…
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Algebraic topology has been extensively and successfully used in image processing for a long time. In telecommunication networks, it can be used to verify that a zone in the plane is fully covered by a set of base stations with a few informations on their relative locations. In this article, we compute some of the…
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Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion. These processes are thus very far from the uncorrelated situation encountered in Poisson models. Quasi-invariance In the linked paper, we establish a quasi-invariance result : we show that if atoms…
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