5 problems

Consider an engulfing version of multi-particle diffusion-limited aggregation (MDLA) with particle density $\lambda$ and internal random-walk rate $\gamma$, where $\gamma=\infty$ m…

Consider the annihilating version of the Pool model, in which excess particles at an attached location are annihilated, and take the particle density at criticality, $\lambda=1$. C…

Consider the Brownian Pool model obtained by replacing the continuous-time and continuous-space random walks in the Pool model by Brownian motion, and let $\lambda=1$ be the critic…

Let $\mathcal{E}_t$ denote the pool radius or size at time $t$ in the Pool model, and let $\lambda$ be the particle density. Critical Pool-model linear-growth conjecture. At the cr…

Let $\lambda>0$ be the particle density in multi-particle diffusion-limited aggregation (MDLA) on $\mathbb{Z}^d$, with $d\theq 2$. MDLA linear-growth conjecture. The aggregate grow…