Rate of Convergence in Homogenization of Parabolic PDEs

We consider the solutions to /tu⁽ⁿ⁾=a⁽ⁿ⁾(x)u⁽ⁿ⁾ where {a⁽ⁿ⁾(x)}_n=1,2,... are random fields satisfying a well-mixing condition (which is different to the usual strong mixing condition). In this paper we estimate the rate of convergence of u⁽ⁿ⁾ to the solution of a heat equation. Since our equation is of simple form, we get quite strong result which covers the previous homogenization results obtained on this equation.