11 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…

Let ${\sf TDLA}_0(n,[0,+\infty)^2)$ be the square DLA tree with $n$ vertices, rooted at the corner ${\bf c}$, and let ${\bf v}$ be a uniformly sampled vertex of the tree. Write…

Let ${sf TDLA}0(n,{ sf Torus}(n^c))$ denote the finite-graph DLA tree with $n$ vertices rooted at $0$, and let ${bf dla}n$ denote the standard DLA tree with $n$ vertices. **The fin…

Let $Z_1,Z_2,\dots$ be independent identically distributed random variables with … and initialize the one-dimensional multi-particle Diffusion Limited Aggregation model with $Z_i$…

Let $(A_n)_{n\geq 0}$ be the DLA cluster process in the wedge $W_{\theta_1,\theta_2}$, and define its growth rate by … where $\operatorname{diam}$ denotes Euclidean diameter, and l…

Let $A_\infty$ be the limiting diffusion-limited aggregation cluster in a wedge, and interpret its arms as the ends of the graph $A_\infty$. One-arm conjecture. There exists…

DLA superminimal growth conjecture.

DLA growth exponent conjecture. There exists $\tfrac{1}{d}<\alpha<1$ such that

Let $t_{\mathrm{end}}$ denote the time at which the diffusion limited aggregation process reaches its terminal stage in the Boolean lattice on $n$ elements. Subexponential end time…

Let $R$ be a transient random walk on $\mathbb{Z}$, and let $A_n$ be the aggregate after $n$ particles. Write $\operatorname{Cap}(A_n)$ for its capacity. Capacity sparsity conjectu…

Let $R$ be a symmetric random walk on $\mathbb{Z}$ with step distribution satisfying … for some $0<\alpha<1$, and let $D_n$ denote the diameter of the aggregate after $n$ particles…