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The accuracy of the forward scattering approximation for two-point Green'sfunctions of the Anderson localization model on the Cayley tree is studied. Arelationship between the moments of the Green's function and the largesteigenvalue of the linearized transfer-matrix equation is proved in theframework of the supersymmetric functional-integral method. The newlarge-disorder approximation for this eigenvalue is derived and its accuracy isestablished. Using this approximation the probability distribution of thetwo-point Green's function is found and compared with that in the forwardscattering approximation (FSA). It is shown that FSA overestimates the role ofresonances and thus the probability for the Green's function to besignificantly larger than its typical value. The error of FSA increases withincreasing the distance between points in a two-point Green's function.

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation