Cell-free DNA (cfDNA) is released into the bloodstream from cells in various physiological
and pathological conditions. The use of cfDNA as a non-invasive biomarker has attracted …

We are interested in the local limits of families of random trees that satisfy the Markov
branching property, which is fulfilled by a wide range of models. Loosely, this property …

We consider a family of fragmentation processes where the rate at which a particle splits is
proportional to a function of its mass. Let F 1 (m)(t), F 2 (m)(t),… denote the decreasing …

We introduce and study two new classes of branching and fragmenting particle systems in
biology. The first class of branching particle systems with interactions model spatially …

We present a further analysis of the fragmentation at heights of the normalized Brownian
excursion. Specifically we study a representation for the mass of a tagged fragment in terms …

This thesis treats stochastic aspects of fragmentation processes when growth and/or
immigration of particles are incorporated as a compensating phenomenon. In a first part, we …

Fragmentation processes describe phenomena of random splitting, with possibly infinite
activity, according to certain rules that give rise to a close relation of these processes to …

Fragmentation is a natural phenomenon that can be observed in many sciences, at a great
variety of scales. To give just a few examples, let us simply mention, the studies of stellar …

In this paper we extend two limit theorems which were recently obtained for fragmentation
processes to such processes with immigration. More precisely, in the setting with …

Merci aussia Brigitte Chauvin, Yves Le Jan et Stéphane Mischler qui me font l'honneur de
faire partie du jury. Stefano Olla a assuré en plus la tâche de coordinateur: je l'en remercie …