5 problems

Recall that $m_i$ is the location of the tree farthest from the origin burnt by the $i$-th fire, and let $f_{m_i,2}$ denote the time when the site $m_i$ is burnt for the second tim…

Let $\varphi(t)$ denote the quantity used in both the critical forest fire equations and the age differential equation to describe the corresponding evolving system. Convergence co…

The mean field forest fire model has big components whose dynamics, after critical scaling, are described by a coagulation-fragmentation process. Let the lightning rate be…

Forest-fire cluster-shape conjecture. In this forest-fire model, typical clusters are again subcritical Galton–Watson trees before gelation and critical Galton–Watson trees past ge…

Consider the forest-fire model on the square lattice, where an original Bernoulli percolation configuration at density $p$ has its infinite cluster removed, and an independent Bern…