3 problems

Let the steady-state cluster conditioned on its size tend to its Benjamini–Schramm limit as the size tends to infinity. Consider the distribution of the fires seen in the long run…

A unimodular graph is a random rooted graph satisfying the mass-transport principle, and a Benjamini–Schramm limit is a local weak limit of finite graphs. Unimodular graph finite-m…

The PSHT is the one-parameter family of full-plane triangulations $\{T_\kappa\}_{\kappa\in(0,2/27)}$ known as the Planar Stochastic Hyperbolic Triangulation. For some…