Random homogenization of coercive Hamilton-Jacobi equations in 1d

In this paper, we will prove the random homogenization of general coercive non-convex Hamilton-Jacobi equations in one dimensional case. This extends the result of Armstrong, Tran and Yu when the Hamiltonian has a separable form $H(p,x,\omega )=H(p)+V(x,\omega )$ for any coercive $H(p)$.