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 end to the other of a segment of a Sinai lattice. In the limit of the length of the lattice segment going to infinity, the distribution of MFPT over Sinai disorder has unbounded moments. We present a multifractal characterization of the distribution. We derive an analytical expression for the fractal dimension as a function of the strength of the disorder. We demonstrate that the multifractality of the limiting distribution manifests itself as self-similar fluctuations of the MFPT from one disorder configuration to the other.