Submitted Abstract
The aim of this project is to combine two outstanding approaches towards probabilistic approximations via the so-called ‘Stein’s method’ – namely the coupling and variational ones – of which Singapore and Luxembourg, respectively, have been creators and worldwide leaders for several years. Such a unification will generate a number of novel theoretical tools, that will be used in order to explore several directions of investigation, at the forefront of current mathematical research. In particular, through the hiring of two post-doctoral fellows, the project’s goal is to merge the efforts of the research groups of L. H. Y. Chen and A. Röllin (Singapore) and of I. Nourdin and G. Peccati (Singapore) in order to attack a number of open problems in modern stochastic analysis, with specific focus on probabilistic approximations for random measures and geometric applications, nodal analysis of random waves, random matrix theory, probabilistic number theory, and applications to life sciences.