The asymptotic-direction conjecture for minimizing geodesics in Euclidean first-passage percolation
Let BnE=BE(0,n)B^{\mathrm{E}}_n=B^{\mathrm{E}}(0,n)BnE=BE(0,n) be the Euclidean ball of radius nnn, let Vn⊆Sd−1\mathcal V_n\subseteq S^{d-1}Vn⊆Sd−1 be the set of initial velocities of minimizing unit-speed geodes…