**Abstract:** | We consider the asymptotic behavior of a quasilinear PDE with mild noise, which originally appears in the hydrodynamic scaling limit of a microscopic interacting particle system called zero-range process in a random environment on one-dimensional discrete lattice. We mainly establish the convergence result of the stochastic quasilinear PDE driven by a mild noise and show the local-in-time well-posedness of the limit stochastic PDE with spatial white noise by the approach of the paracontrolled calculus. For a special case, we also show the global-in-time solvability and the convergence of the solution to its stationary solution for long time. This talk is partially based on the joint work with T. Funaki, M. Hoshino and S. Sethuraman. |