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                <term xml:lang="en">Log-concavity</term>
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                <term xml:lang="fr">Log-concavité</term>
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              <p>Cette thèse s'inscrit dans le cadre des probabilités en grande dimension, en particulier sous hypothèse de convexité. Dans une première partie, on étudie le comportement des l'entropie et de l'information de Fisher vis à vis des convolutions de vecteurs log-concave. Ensuite, à l'aide de la localisation stochastique, une technique récente qui a notamment servi à la quasi résolution de la conjecture KLS, nous établissons des résultats nouveaux sur la fonction de concentration des mesures log-concave, et leur constante de log-sobolev. La dernière partie est consacrée à l'étude de grands systèmes linéaires aléatoires pour lesquels un phénomène de type cut-off est démontré.</p>
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