3 problems

Kapri–Dhar conjecture. The set of sites visited by the clockwise uniform rotor walk in $t$ steps is asymptotically a disk of average radius

Consider the asymptotic shape in planar first-passage percolation and the critical angle for survival from cone-shaped initial conditions in direction $\theta$. Asymptotic-shape di…

Asymptotic shape conjecture. There exists a bounded convex set $U\subset\mathds{R}^d$ such that, for every $\varepsilon>0$,