Contributions à l'étude de modèles biologiques, d'inégalités fonctionnelles, et de matrices aléatoires

Abstract : The presented works concern three autonomous topics :

(1) Biological models and Statistics : comparmental models, population pharmacokinetics and pharmacodynamics, estimators for stochastic inverse problems, nonlinear mixed effects models, mixture models, EM and ICF type algorithms, graphical covariance models, modelling in Cancerology, point processes and particles, queueing systems, Feynman-Kac formulas

(2) Functional inequalities: Sobolev type inequalities, concentration of measure, isoperimetry, role of convexity in entropic inequalities, tensorization, heat kernels, Heisenberg group and hypoelliptic dynamics, queueing systems, mixtures of distributions

(3) Random matrices: spectrum of random Markov matrices, graphs with random weights, Wigner, Marchenko-Pastur, and Girko-Bai type theorems, convergence of extremal eigenvalues, rank one deformations.

The most frequent concept here is the notion of Markov dynamics. In the first part, the compartmental models give rise to such dynamics. The second part is related to the geometry and trend to equilibrium of Markov dynamics. The third part is devoted to random Markov dynamics. However, these three parts cannot be reduced to the study of certain aspects of Markov dynamics. The content ranges from concrete applications to abstract theoretical problems, and makes use of various concepts and techniques from Mathematical Analysis, Probability Theory and Statistics.
Document type :
Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00346998
Contributor : Djalil Chafaï <>
Submitted on : Saturday, December 13, 2008 - 10:48:46 AM
Last modification on : Wednesday, February 19, 2020 - 2:29:49 PM
Long-term archiving on: Thursday, October 11, 2012 - 1:36:25 PM

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  • HAL Id : tel-00346998, version 1

Citation

Djalil Chafai. Contributions à l'étude de modèles biologiques, d'inégalités fonctionnelles, et de matrices aléatoires. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2008. ⟨tel-00346998⟩

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