Abstract Alexis Prevost: I will review recent results concerning the phase transition for a strongly correlated percolation model called the metric graph Gaussian free field. In particular, I will focus on the critical exponents which describe the volume of a critical connected component on graphs of intermediate dimension. Joint work with Alexander Drewitz and Pierre-François Rodriguez. / Abstract Matteo D'Achille: We will discuss limits in low intensity of Poisson-Voronoi tessellations, called ideal Poisson-Voronoi tessellations (IPVTs). The main focus of the talk will be the IPVT of hyperbolic space*, but I will also discuss IPVTs on other metric spaces, such as Cartesian products of hyperbolic spaces and horocyclic products of regular trees (a.k.a. Diestel-Leader graphs). Talk based on a joint work with Nicolas Curien, Nathanaël Enriquez, Russell Lyons, Meltem Ünel (2303.16831), on a forthcoming work and on a work in progress with Ali Khezeli. *Featuring 3D-printed realizations of a cell of the IPVT on 3-dimensional hyperbolic space in the Poincaré ball model.