Étude des maxima de champs gaussiens corrélés
In this study, results about maxima of different Gaussian fields will be presented. More precisely, results for the convergence of the first order of the maximum of a set of Gaussian variables will be presented. Some results on the convergence of the second order, and of the law will also be explained. The models presented here are the Gaussian field of i.i.d. variables, the hierarchical model and the Gaussian free fields model. These fields differ from one another by their correlation structure. The main result of this study is that the first order convergence in probability of the maximum is the same for the three models. Finally, numerical simulations results will be presented to confirm theoretical results.
Maxima Gaussian free field Hierarchical model Random walk