Random Geometry and Physics, why and how?

During the last century, probability theory deeply reshaped physics but its influence on geometry was smaller. However from condensed matter to quantum field theory and quantum gravity, from disordered media to polymer, spin glasses, foams and membranes, many important physical problems today increasingly combine randomness to geometry in some way or another. We shall attempt a general introduction to this growing interface between geometry, probability theory and physics and then focus on a few recent mathematical tools such as Gromov–Hausdorff convergence, Brownian spheres and random tensors, which could help us to better discretize and handle such physical problems.