28 problems

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…

Sublinear layer-hitting time conjecture. For every such family of regular graphs, the expected time for the cluster to reach layer $m$ is at most $m|G_n|^\gamma$ for some fixed exp…

Let $A\subset\mathbb{Z}^d$ be the region formed by iteratively adjoining to $A$ the terminus of a random walk beginning at infinity and ending when first adjacent to $A$. Barlow's…

Let $\mathcal{G}$ be a graph with fields $\phi_i,\tilde\phi_i$ describing branching trees, and let $\mathfrak{r}$ and $\mathfrak{t}$ be graph points. Write…

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 $\lambda>0$ 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…

Irregular-cluster conjecture. DBM also produces irregular clusters in a similar manner to DLA.

Uniqueness conjecture. In a thin enough linear wedge, the DLA cluster has only one infinite arm.

In dimension $d$, let $\alpha$ denote the growth exponent governing the characteristic linear size of a DLA cluster with $n$ particles, so that the relevant size scales as…

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…

Fix … be a limit point of an external multi-particle diffusion-limited aggregation process, with associated absorbed Brownian motion density $u$ and occupied region … partialt u=fr…

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 $Z_i$…

Near-critical speed conjecture. As $\lambda\searrow1$,

In the one-dimensional multi-particle Diffusion Limited Aggregation model, let $X_t$ denote the size of the aggregate at time $t$. Critical growth exponent conjecture. At the criti…

Let DLA denote diffusion-limited aggregation and let the border aggregation model be the model obtained by growing inward from a prescribed boundary. On the square lattice…

The diffusion-limited aggregation (DLA) process started from a long line segment is expected to have a distinct fractal dimension from standard DLA started at a point. The scaling…

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 $d\geq 2$ and let $K$ be the mean Poisson density of particles in the $d$-dimensional multi-particle diffusion-limited aggregation model. Let the critical value be the density…

Let $K$ be the mean Poisson density of particles in the multi-particle diffusion-limited aggregation model, and let the critical value mean the density threshold above which the ag…

Let $K$ be the mean Poisson density of independently moving particles in the one-dimensional multi-particle diffusion-limited aggregation model, and let $X_t$ denote the rightmost…