9 problems

Uniform boundedness conjecture. There is a constant $\delta$ such that

Let $R(t)$ and $B(t)$ be the red and blue regions of the two-species competition model, and let $\mathcal{S}$ be the Richardson-model limit shape. For a subset…

Consider the competition process on $\mathbb{Z}^d$ with blue and yellow infections, whose transmission parameters are $p_{\text{b}}$ and $p_{\text{y}}$, respectively. Let $p_c$ be…

Let $\sigma>0$ be the ultraviolet cutoff in the Hele–Shaw problem, let $\kappa(\gamma)$ denote the boundary curvature at the boundary parameter $\gamma$, and consider the limit…

Let $d\geq 2$. Consider the two-type Richardson model on $\mathbb{Z}^d$, with $FPP_1$ initialized at the origin and $FPP_{\lambda}$ spreading from a single seed activated at time…

Let ORRW and OERW denote the two growth models discussed in the source, with evolution indexed by time. Asymptotic shape conjecture. For both ORRW and OERW, the evolution should le…

Häggström–Pemantle conjecture. The event $$ has positive probability if and only if $\lambda=1$.

Consider a $(2+1)$-dimensional growth model with characteristic lines determined by the Hamilton–Jacobi equation governing its macroscopic height profile. Let height fluctuations a…

Let $v(\cdot)$ be the speed function of a reasonable $(2+1)$-dimensional growth model, and let $H_\rho$ be the Hessian of $v(\cdot)$ computed at the slope $\rho$. Write $\alpha$ fo…