MULTIFRACTAL SCALING OF MOMENTS OF MEAN FIRST-PASSAGE TIME IN THE PRESENCE OF SINAI DISORDER

We consider mean first-passage time (MFPT) of random walks from one en d to the other of a segment of a Sinai lattice. In the limit of the le ngth of the lattice segment going to infinity, the distribution of MFP T over Sinai disorder has unbounded moments. We present a multifractal characterization of the distribution. We derive an analytical express ion for the fractal dimension as a function of the strength of the dis order. We demonstrate that the multifractality of the limiting distrib ution manifests itself as self-similar fluctuations of the MFPT from o ne disorder configuration to the other.