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]

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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