5 problems

Fix $\alpha\in(1,2)$. Let $T_n^{(\alpha)}$ be a critical Bienaymé–Galton–Watson tree with offspring distribution $\mu_\alpha$ satisfying $\mu_\alpha([x,\infty))\sim cx^{-\alpha}$ a…

The paper studies random quadrangulations obtained from critical Bienaymé–Galton–Watson trees whose offspring distribution has a stably decaying tail with exponent $\alpha\in(1,2)$…

Distribution conjecture. The pair $({\rm Sch}_\infty,\Delta h)$ is distributed as a Galton–Watson tree with geometric-$1/2$ offspring distribution, conditioned to be infinite, with…

Local convergence conjecture. The pair

Connectivity conjecture. The graph ${\rm Sch}_\infty(Q)$ is connected almost surely.