If you want to apply for a PhD thesis, the best is to start doing an internship.
I am happy to offer internships to students. If you want to apply for an internship, please send me the contact of at least one person who can recommend you (a faculty member of your university or a person with whom you have worked).
List of possible subjects:
Other subject related to the previous ones can also be proposed. For example
Keywords : stochastic networks, mean-field limit, stochastic optimization
Stochastic models of interacting agents are used in many domains (caching systems, networks,...). The analysis of the model of n stochastic entities interacting with each others can be particularly difficult. The mean field approximation is a very effective technique to characterize the transient probability distribution or steady-state regime of such systems when the number of entities n grows very large. The idea of mean-field approximation is to replace a complex stochastic system by a simpler deterministic dynamical system. Our recent progress suggest that it is possible to extend these methods to study systems with a relatively small entities (n=10). The objective of the post-doc will be to contribute to the development of theoretical and analytical tools on this subject, for example to focus on heavy-traffic regime and heterogeneous systems.
Depending on the candidate, this project can have a more theoretical flavour or a more algorithmic one. Different applications are envisioned.