Non-bijective scaling limit of maps via restrictions.

Abstract: In recent years, scaling limits of random planar maps have been the subject of a lot of attention. So far, the convergence of these random combinatorial objects relies heavily on bijections. In this talk, I will present a non-bijective technique that allows to obtain the convergence of a random map model, using a convergent closely related random map model. Then, I will present a new result which is obtained using our technique: the Brownian disk is the limit of quadrangulations with a simple boundary, when the boundary is of order (faces^{1/2}).