This class aims at understanding some important classes of smooth random functions of very many variables.
What can be said about the complexity of the topology of the landscapes they define?
How efficient are the natural exploration or optimization algorithms in these landscapes?
The toolbox of Random Matrix Theory will be used for both questions.
We will concentrate on two wide classes of interesting smooth random functions of many variables.
A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.
Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.No Notes/Supplements Uploaded No Video Files Uploaded