Quenched Central Limit Theorem in a Corner Growth Setting.

@article{Gromoll2018QuenchedCL,
title={Quenched Central Limit Theorem in a Corner Growth Setting.},
author={H. C. Gromoll and Mark W. Meckes and L. Petrov},
journal={arXiv: Probability},
year={2018}
}

We consider point-to-point directed paths in a random environment on the two-dimensional integer lattice. For a general independent environment under mild assumptions we show that the quenched energy of a typical path satisfies a central limit theorem as the mesh of the lattice goes to zero. Our proofs rely on concentration of measure techniques and some combinatorial bounds on families of paths.