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Some recent developments in the theory of fragmentations.

Abstract : The main subject of this PHD thesis is the study of various quantities related to fragmentation processes. These processes are designed to modelize a unit mass object which fragments with time.
This work is composed of four chapters. The aim of the first one is to study the Hausdorff dimension of the set of locations having exactly an exponential decay. In the second chapter, we construct a self-similar Markov process which generalizes the classical fragmentation by allowing in particular the size of the descendants to be bigger than the one of their parents. Then we show some Limit Theorems using the theory of self-similar Markov processes. In the third chapter, we are interested by the statistical estimation of the Lévy measure of the classical subordinator associated to the fragmentation. More precisely, we observe the fragments only when their size reach a size smaller than a given threshold. Finally, in the fourth chapter, we study the energy cost of a succession of fragmentations.
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Contributor : Nathalie Krell <>
Submitted on : Thursday, July 3, 2008 - 2:44:31 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:44 PM
Long-term archiving on: : Friday, May 28, 2010 - 11:08:22 PM


  • HAL Id : tel-00293022, version 1


Nathalie Krell. Some recent developments in the theory of fragmentations.. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2008. English. ⟨tel-00293022⟩



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