4 problems

Existence conjecture. The limit $\lim_{n\to\infty}Z_n$ exists, at least in probability.

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…

Let $v_k^n(t)$ be the random proportion of vertices at time $t$ that belong to clusters of size $k$ under the stationary law $\mathbb{P}_{\mathrm{stat}}^n$, and let…

Let $\mathcal{C}(t)$ be the steady state cluster growth process, and let the mean field forest fire model of Ráth and Tóth evolve in its stationary state. Consider the cluster cont…