# Quenched Central Limit Theorem in a Corner Growth Setting

### 2018/04/12

(with Christian Gromoll, Mark Meckes)
arXiv:1804.04222 [math.PR]

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.

A histogram of the path energies ‐ the original motivation for the work