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The article begins with a quantitative version of the martingale centrallimit theorem, in terms of the Kantorovich distance. This result is then usedin the study of the homogenization of discrete parabolic equations with randomi.i.d. coefficients. For smooth initial condition, the rescaled solution ofsuch an equation, once averaged over the randomness, is shown to convergepolynomially fast to the solution of the homogenized equation, with an explicitexponent depending only on the dimension. Polynomial rate of homogenization forthe averaged heat kernel, with an explicit exponent, is then derived. Similarresults for elliptic equations are also presented.

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients