Processus d’exploration des arbres aléatoires en temps continu à branchement non binaire. Limite en grande population.

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Date/heure
Date(s) - 22/05/2017
13 h 30 min - 15 h 30 min

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In this thesis, we study the convergence of the exploration process of the non-binary tree associated to a continuous time branching process, in the limit of a large population. In the first part, we give a precise description of the exploration process of the non-binary tree. We then describe a bijection between exploration processes and Galton Watson non-binary trees. After some renormalization, we present the results of convergence of the population process and the exploration process, in the limit of a large populations.In the second part, we first establish the convergence of the population process to a continuous state branching process (CSBP) with jumps. We then show the convergence of the (rescaled) exploration process, of the corresponding genealogical tree towards the continuous height process recently defined by Li, Pardoux and Wakolbinger. In the last part, we consider a population model with interaction defined with a more general non linear function. We proceed to a renormalization of the parameters model and we obtain in limit a generalized CSBP. We then renormalize the height process of the associated genealogical tree, and take the weak limit as the size of the population tends to infinity.

*Membres du jury :


Vincent BANSAYE, Ecole Polytechnique de Paris, Rapporteur
Romain ABRAHAM, Université d’Orléans, Examinateur
Ahmadou Bamba SOW, Université Gaston Berger du Sénégal, Codirecteur
Etienne PARDOUX, Aix-Marseille Universite, Directeur
Thomas DUQUESNE, Université Pierre et Marie Curie, Rapporteur
Anton WAKOLBINGER, J. W. Goethe Universitat, Germany, Examinateur

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Liens :
Université Gaston Berger – Saint-Louis du Sénégal (cotutelle)
theses.fr

Olivier CHABROL
Posts created 14

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