Nicolas Gast - Refinements of Mean Field Approximation

The design of efficient algorithms is closely linked to the evaluation of their performances. My work focuses on the use of stochastic models for the performance evaluation of large distributed systems.  I am interested in developing tools that can characterize the emergent behavior of such systems and improve their performance. This leads me to solve stochastic control and optimization problems, notably through operations research methods. These problems suffer from combinatorial explosion: the complexity of a problem grows exponentially with the number of objects that compose it. It is therefore necessary to design models but also algorithmic processes whose complexity does not increase too rapidly with the size of the system.

In this presentation, I will summarize a few of my contributions on the use and the refinements of mean field approxiamtion to study the performance of distributed systems and algorithms.  I will introduce the key concepts behind mean field approximation, by giving some examples of where it can be applied. I will review some of the classical models and try to answer a very natural question: how large should a system be for mean field to apply?

Vous pouvez lire le manuscrit de cette HDR.