Sublinear variance for directed last-passage percolation
arXiv:0909.1352
Abstract
A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the `directed polymers in a random environment' model.
Revised version. Accepted: Journal of Theoretical Probability