# Quenched Central Limit Theorem in a Corner Growth Setting

### 2018/04/12

Christian Gromoll,

Mark Meckes, Leonid Petrov

*Electronic Communications in Probability (2018), Vol. 23, paper no. 101, 1-12* •

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